Boundary S-Matrix and Boundary State in Two-Dimensional Integrable Quantum Field Theory

Abstract

We study integrals of motion and factorizable S-matrices in two-dimensional integrable field theory with boundary. We propose the ``boundary cross-unitarity equation'' which is the boundary analog of the cross-symmetry condition of the ``bulk'' S-matrix. We derive the boundary S-matrices for the Ising field theory with boundary magnetic field and for the boundary sine-Gordon model.

44pp, RU-93-20

Cited by in corpus (639)

• Nonequilibrium dynamics of closed interacting quantum systems
• Integrable Structure of Conformal Field Theory, Quantum KdV Theory and Thermodynamic Bethe Ansatz
• Quantum Quench in the Transverse Field Ising chain I: Time evolution of order parameter correlators
• Exact Conductance through Point Contacts in the $\nu =1/3$ Fractional Quantum Hall Effect
• Exact non-equilibrium transport through point contacts in quantum wires and fractional quantum Hall devices
• On the Boundary Entropy of One-dimensional Quantum Systems at Low Temperature
• Conformal description of horizon's states
• Quantum Quenches in Integrable Field Theories
• Boundary Conditions in Rational Conformal Field Theories
• What is an integrable quench?
• Boundary energy and boundary states in integrable quantum field theories
• The quark anti-quark potential and the cusp anomalous dimension from a TBA equation
• Bethe Ansatz solution of the open XXZ chain with nondiagonal boundary terms
• Exact solution of a massless scalar field with a relevant boundary interaction
• Long time dynamics following a quench in an integrable quantum spin chain: local versus non-local operators and effective thermal behavior
• Bra-ket wormholes in gravitationally prepared states
• Exact ground states and topological order in interacting Kitaev/Majorana chains
• Exact non-equilibrium DC shot noise in Luttinger liquids and fractional quantum Hall devices
• Linear response theory for a pair of coupled one-dimensional condensates of interacting atoms
• Introduction to Yangian symmetry in integrable field theory
• Functional relations and Bethe Ansatz for the XXZ chain
• Quantum quench in the sine-Gordon model
• Classically integrable boundary conditions for affine Toda field theories
• Reflection and Transmission for Conformal Defects
• Exact spectrum of the XXZ open spin chain from the q-Onsager algebra representation theory
• Integrable structure of W_3 Conformal Field Theory, Quantum Boussinesq Theory and Boundary Affine Toda Theory
• Scattering Theory and Correlation Functions in Statistical Models with a Line of Defect
• XXZ chain with a boundary
• Quantum quenches in the anisotropic spin-1/2 Heisenberg chain: different approaches to many-body dynamics far from equilibrium
• Dynamics in the Ising field theory after a quantum quench
• Interaction-Round-a-Face Models with Fixed Boundary Conditions: The ABF Fusion Hierarchy
• Antiperiodic spin-1/2 XXZ quantum chains by separation of variables: Complete spectrum and form factors
• Integrable Wilson loops
• Off-diagonal Bethe ansatz solutions of the anisotropic spin-1/2 chains with arbitrary boundary fields
• Entanglement and boundary critical phenomena
• Solving the open XXZ spin chain with nondiagonal boundary terms at roots of unity
• Functional relations from the Yang-Baxter algebra: Eigenvalues of the XXZ model with non-diagonal twisted and open boundary conditions
• Completeness of the Bethe Ansatz solution of the open XXZ chain with nondiagonal boundary terms
• Supersymmetry in Boundary Integrable Models
• Integrable XYZ Spin Chain with Boundaries
• TBA and TCSA with boundaries and excited states
• Correlation functions of the open XXZ chain I
• Off-diagonal Bethe ansatz solution of the XXX spin-chain with arbitrary boundary conditions
• Difference Equations in Spin Chains with a Boundary
• Classically integrable field theories with defects
• Reflecting magnons
• Super Liouville Theory with Boundary
• An integrable structure related with tridiagonal algebras
• Purely Transmitting Defect Field Theories
• Deformed Dolan-Grady relations in quantum integrable models
• Spectroscopy of Collective Excitations in Interacting Low-Dimensional Many-Body Systems Using Quench Dynamics
• Heisenberg XXX Model with General Boundaries: Eigenvectors from Algebraic Bethe Ansatz
• A new (in)finite dimensional algebra for quantum integrable models
• Q-operator and T-Q relation from the fusion hierarchy
• g-function flow in perturbed boundary conformal field theories
• Integrable Floquet dynamics
• Scalar one-point functions and matrix product states of AdS/dCFT
• Analytic Solution of Bremsstrahlung TBA
• Boundary interactions changing operators and dynamical correlations in quantum impurity problems
• Surface excitations and surface energy of the antiferromagnetic XXZ chain by the Bethe ansatz approach
• Integrable vertex and loop models on the square lattice with open boundaries via reflection matrices
• Exact One-Point Function of N=1 super-Liouville Theory with Boundary
• Zamolodchikov-Faddeev Algebra and Quantum Quenches in Integrable Field Theories
• Row Transfer Matrix Functional Relations for Baxter's Eight-Vertex and Six-Vertex Models with Open Boundaries Via More General Reflection Matrices
• Boundary bound states and boundary bootstrap in the sine-Gordon model with Dirichlet boundary conditions.
• Correlation Functions of the Quantum Sine-Gordon Model in and out of Equilibrium
• Non-equilibrium DC noise in a Luttinger liquid with impurity
• Quantum quenches in the sinh-Gordon model: steady state and one point correlation functions
• Correlation functions of the open XXZ chain II
• Integrable Model of Boundary Interaction: The Paperclip
• Exact Three-Point Functions of Determinant Operators in Planar N=4 Supersymmetric Yang-Mills Theory
• Initial states in integrable quantum field theory quenches from an integral equation hierarchy
• Boundary remnant of Yangian symmetry and the structure of rational reflection matrices
• The quantum sine-Gordon model with quantum circuits
• Boundary Critical Phenomena in the Three-State Potts Model
• Mean values of local operators in highly excited Bethe states
• Boundary State in an Integrable Quantum Field Theory Out of Equilibrium
• Expectation values of boundary fields in the boundary sine-Gordon model
• Overlaps after quantum quenches in the sine-Gordon model
• Integrable approach to simple exclusion processes with boundaries. Review and progress
• Statistics of the work done by splitting a one-dimensional quasi-condensate
• Some aspects of jump-defects in the quantum sine-Gordon model
• Non-perturbative Defect One-Point Functions in Planar $\mathcal{N}=4$ Super-Yang-Mills
• Edge Critical Behaviour of the 2-Dimensional Tri-critical Ising Model
• Realization of 2-channel Kondo effect in a junction of three quantum Ising chains
• Bi-partite entanglement entropy in massive QFT with a boundary: the Ising model
• General boundary conditions for the sl(N) and sl(M|N) open spin chains
• Crossover physics in the non-equilibrium dynamics of quenched quantum impurity systems
• Algebraic Bethe ansatz for eight vertex model with general open-boundary conditions
• Boundary flows in minimal models
• Universal low-temperature crossover in two-channel Kondo models
• Exact solution of the XXZ Gaudin model with generic open boundaries
• Conformal perturbation theory beyond the leading order
• Scattering in the Presence of a Reflecting and Transmitting Impurity
• Fractional-Spin Integrals of Motion for the Boundary Sine-Gordon Model at the Free Fermion Point
• Boundary Flows in general Coset Theories
• A unified framework for the Kondo problem and for an impurity in a Luttinger liquid
• The open XXX spin chain in the SoV framework: scalar product of separate states
• Form factors approach to current correlations in one dimensional systems with impurities
• Bi-partite entanglement entropy in massive 1+1-dimensional quantum field theories
• Reflection-Transmission Algebras
• Affine Toda field theories with defects
• Time correlations in 1D quantum impurity problems
• Bulk and Boundary S Matrices for the SU(N) Chain
• Solving topological defects via fusion
• Open Spin Chain and Open Spinning String
• Exact crossover Green function in the two-channel and two-impurity Kondo models
• String field theory vertex from integrability
• Boundary states, overlaps, nesting and bootstrapping AdS/dCFT
• Integrable quantum field theory with boundaries: the exact g-function
• The Josephson current in Luttinger liquid-superconductor junctions
• Inhomogeneous T-Q equation for the open XXX chain with general boundary terms: completeness and arbitrary spin
• From Defects to Boundaries
• Solutions of the reflection equation for face and vertex models associated with $A_n^{(1)},B_n^{(1)},C_n^{(1)},D_n^{(1)}$ and $A_n^{(2)}$
• Structure Constants in $\mathcal{N}=4$ SYM at Finite Coupling as Worldsheet $g$-Function
• Sailing past the End of the World and discovering the Island
• Antiperiodic dynamical 6-vertex model I: Complete spectrum by SOV, matrix elements of the identity on separate states and connections to the periodic 8-vertex model
• Quantum spin chain with "soliton non-preserving" boundary conditions
• One-point functions in massive integrable QFT with boundaries
• Dynamics of charge fluctuations from asymmetric initial states
• Integrable Matrix Product States from boundary integrability
• Functional Bethe ansatz methods for the open XXX chain
• Exact solution of the open XXZ chain with general integrable boundary terms at roots of unity
• Magnetization and dimerization profiles of the cut two-leg spin ladder and spin-1 chain
• Floquet Dynamics of Boundary-Driven Systems at Criticality
• On the second reference state and complete eigenstates of the open XXZ chain
• Andreev reflection in the fractional quantum Hall effect
• Supersymmetric extension of the sine-Gordon theory with integrable boundary interactions
• Bethe states of the XXZ spin-1/2 chain with arbitrary boundary fields
• Quench dynamics of the Ising field theory in a magnetic field
• Fused integrable lattice models with quantum impurities and open boundaries
• Integrable Open Spin Chain in Super Yang-Mills and the Plane-wave/SYM duality
• Generalisations of the Coleman-Thun mechanism and boundary reflection factors
• Sine-Gordon quantum field theory on the half-line with quantum boundary degrees of freedom
• The k-folded sine-Gordon model in finite volume
• Form factors and complete spectrum of XXX antiperiodic higher spin chains by quantum separation of variables
• Boundary spectrum in the sine-Gordon model with Dirichlet boundary conditions
• Reflection K-Matrices for 19-Vertex Models
• Nonequilibrium Transport through Double Quantum Dots: Exact Results near Quantum Critical Point
• The boundary supersymmetric sine-Gordon model revisited
• Transfer matrix spectrum for cyclic representations of the 6-vertex reflection algebra I
• Solving 1d plasmas and 2d boundary problems using Jack polynomials and functional relations
• Three aspects of bosonized supersymmetry and linear differential field equation with reflection
• Bethe Ansatz derived from the functional relations of the open XXZ chain for new special cases
• Duality and quantum-algebra symmetry of the A_{N-1}^(1) open spin chain with diagonal boundary fields
• Overlap singularity and time evolution in integrable quantum field theory
• Hecke algebraic approach to the reflection equation for spin chains
• Spontaneous symmetry breaking in the gl(N)-NLS hierarchy on the half line
• Reflection factors and a two-parameter family of boundary bound states in the sinh-Gordon model
• Boundary Sine-Gordon Interactions at the Free Fermion Point
• On the boundary form factor program
• Fermionic CFTs and classifying algebras
• Boundary quantum group generators of type A
• Finite size effects in boundary sine-Gordon theory
• On duality and reflection factors for the sinh-Gordon model
• From affine Hecke algebras to boundary symmetries
• Separation of Variables in AdS/CFT: Functional Approach for the Fishnet CFT
• Point contact tunneling in the fractional quantum Hall effect: an exact determination of the statistical fluctuations
• Direct Calculation of the Boundary $S$ Matrix for the Open Heisenberg Chain
• The Exact S-Matrix for an osp(2|2) Disordered System
• Bulk flows in Virasoro minimal models with boundaries
• Baxterized Solutions of Reflection Equation and Integrable Chain Models
• Reflection K-Matrices of the 19-Vertex Model and XXZ Spin-1 Chain with General Boundary Terms
• Shot noise in the self-dual Interacting Resonant Level Model
• Non-diagonal solutions to reflection equations in $su(n)$ spin chains
• Edge exponents in work statistics out of equilibrium and dynamical phase transitions from scattering theory in one dimensional gapped systems
• On the form factors of local operators in the Bazhanov-Stroganov and chiral Potts models
• Phase separation in a wedge. Exact results
• Universal Dynamics of Stochastically Driven Quantum Impurities
• Classification of reflection matrices related to (super) Yangians and application to open spin chain models
• Analytical Bethe Ansatz for closed and open gl(n)-spin chains in any representation
• The XX--model with boundaries. Part I: Diagonalization of the finite chain
• Integrable quenches in nested spin chains I: the exact steady states
• Boundary Entropy Can Increase Under Bulk RG Flow
• Low-temperature nonequilibrium transport in a Luttinger liquid
• One-point functions in perturbed boundary conformal field theories
• Anisotropic Spin-1/2 Heisenberg Chain with Open Boundary Conditions
• Reversible Fluxon Logic: Topological particles allow ballistic gates along 1D paths
• The spectrum of boundary states in sine-Gordon model with integrable boundary conditions
• Fusion Hierarchy and Finite-Size Corrections of $U_q[sl(2)]$ Invariant Vertex Models with Open Boundaries
• Quench echo and work statistics in integrable quantum field theories
• The two-boundary sine-Gordon model
• Exact diagonalization of the quantum supersymmetric $S{U}_q(n|m)$ model
• Perturbation of infra-red fixed points and duality in quantum impurity problems
• $A_{n-1}$ Gaudin model with open boundaries
• Entanglement in quantum impurity problems is non perturbative
• Defects in the Tri-critical Ising model
• Finite size effects in the XXZ and sine-Gordon models with two boundaries
• Integrable Circular Brane Model and Coulomb Charging at Large Conduction
• Complete Bethe Ansatz solution of the open spin-s XXZ chain with general integrable boundary terms
• Exact S-matrices for supersymmetric sigma models and the Potts model
• Exact Friedel oscillations in the g=1/2 Luttinger liquid
• Quantum Field Theory, Bosonization and Duality on the Half Line
• Growth of entanglement of generic states under dual-unitary dynamics
• Edge Magnetic Field in the xxz Spin-1/2 Chain
• Minimal model boundary flows and c=1 CFT
• On $A_{n-1}^{(1)},B_n^{(1)},C_n^{(1)},D_n^{(1)},A_{2n}^{(2)},A_{2n-1}^{(2)}$ and $D_{n+1}^{(2)}$ Reflection $K$-Matrices
• The statistical mechanics of the classical two-dimensional Coulomb gas is exactly solved
• Boundary Yang-Baxter equation in the RSOS/SOS representation
• Comments on the Boundary Scattering Phase
• Nonequilibrium Critical Behavior for Electron Tunneling through Quantum Dots in an Aharonov-Bohm Circuit
• Spin Chains with Non-Diagonal Boundaries and Trigonometric SOS Model with Reflecting End
• Bethe Ansatz solution of the open XX spin chain with nondiagonal boundary terms
• Magnetic Fields and Fractional Statistics in Boundary Conformal Field Theory
• Notes on parafermionic QFT's with boundary interaction
• Quantum Electronic Circuit Simulation of Generalized sine-Gordon Models
• Quasi-classical descendants of disordered vertex models with boundaries
• Exact solution of $Z_n$ Belavin model with open boundary condition
• On O(1) contributions to the free energy in Bethe Ansatz systems: the exact g-function
• Boundary Reflection Matrix in Perturbative Quantum Field Theory
• Yangian symmetry and bound states in AdS/CFT boundary scattering
• Open two-species exclusion processes with integrable boundaries
• Boundary ABF Models
• Coupling integrable field theories to mechanical systems at the boundary
• Boundary scattering in the ${\varphi }^6$ model
• Classical Integrable Super sinh-Gordon equation with defects
• On factorized overlaps: Algebraic Bethe Ansatz, twists, and Separation of Variables
• One-point functions in AdS/dCFT
• Universal K-matrices for quantum Kac-Moody algebras
• On boundary RG-flows in coset conformal field theories
• Integrable domain walls in ABJM theory
• Consistent superconformal boundary states
• Quantum quench in the attractive regime of the sine-Gordon model
• Minimal Models with Integrable Local Defects
• From integrability to conductance, impurity systems
• Preparing exact eigenstates of the open XXZ chain on a quantum computer
• Loschmidt Amplitude and Work Distribution in Quenches of the Sine-Gordon Model
• Exact solution of the $A_{n-1}^{(1)}$ trigonometric vertex model with non-diagonal open boundaries
• Finite size effects in quantum field theories with boundary from scattering data
• Boundary RG Flow Associated with the AKNS Soliton Hierarchy
• Local conservation laws in spin-1/2 XY chains with open boundary conditions
• Diagonally and antidiagonally symmetric alternating sign matrices of odd order
• Bethe ansatz of the open spin-s XXZ chain with nondiagonal boundary terms
• A new class of integrable defects
• Twenty-five years of two-dimensional rational conformal field theory
• SOV approach for integrable quantum models associated to general representations on spin-1/2 chains of the 8-vertex reflection algebra
• Correlation functions of the half-infinite XXZ spin chain with a triangular boundary
• The open XXZ and associated models at q root of unity
• The Zamolodchikov-Faddeev algebra for open strings attached to giant gravitons
• On integrable Hamiltonians for higher spin XXZ chain
• Particle Reflection Amplitudes in a_n^(1) Toda Field Theories
• Entanglement Dynamics after a Quench in Ising Field Theory: A Branch Point Twist Field Approach
• Inter edge Tunneling in Quantum Hall Line Junctions
• On a_2^(1) Reflection Matrices and Affine Toda Theories
• Boundary TBA, trees and loops
• Integrable boundary conditions for classical sine-Gordon theory
• Semi-classical theory for quantum quenches in the O(3) non-linear sigma model
• Reflection factors and exact g-functions for purely elastic scattering theories
• Correlations in one dimensional quantum impurity problems with an external field
• Maxwell-Chern-Simons Theory With Boundary
• Yangian symmetric correlators
• Boundary states and finite size effects in sine-Gordon model with Neumann boundary condition
• Integrable Boundary Conditions and Reflection Matrices for the O(N) Nonlinear Sigma Model
• Solutions of the boundary Yang-Baxter equation for arbitrary spin
• Coideal algebras from twisted Manin triples
• Boundary form factors in finite volume
• Semiclassical analysis of defect sine-Gordon theory
• The Bethe Ansatz Equations for Reflecting Magnons
• Quantum affine reflection algebras of type d_n^(1) and reflection matrices
• Spectrum of boundary states in N=1 SUSY sine-Gordon theory
• Quantum integrability in two-dimensional systems with boundary
• Crosscap States in Integrable Field Theories and Spin Chains
• Appearance of ferroelectricity in thin films of incipient ferroelectric
• The open XXZ spin chain in the SoV framework: scalar product of separate states
• Is the Two-Dimensional One-Component Plasma Exactly Solvable?
• Integrable quenches in nested spin chains II: fusion of boundary transfer matrices
• Finite size corrections for open strings/open chains in planar AdS/CFT
• On perturbative quantum field theory with boundary
• Excited states NLIE for sine-Gordon model in a strip with Dirichlet boundary conditions
• On exact overlaps in integrable spin chains
• $C_n^{(1)}$, $D_n^{(1)}$ and $A_{2n-1}^{(2)}$ reflection K-matrices
• Fields, particles and universality in two dimensions
• Entanglement Hamiltonian of the 1+1-dimensional free, compactified boson conformal field theory
• Breaking integrability at the boundary: the sine-Gordon model with Robin boundary conditions
• Correlation spreading and properties of the quantum state in quench dynamics
• Exact boundary S-matrices of the supersymmetric sine-Gordon theory on a half line
• Integrable open spin-chains in AdS3/CFT2 correspondences
• The sine-Gordon model from coupled condensates: a Generalized Hydrodynamics viewpoint
• Resistively shunted Josephson junctions: QFT predictions versus MC results
• NLIE for hole excited states in the sine-Gordon model with two boundaries
• Quantum impurity in a Luttinger liquid: Exact solution of the Kane-Fisher model
• Degenerate operators in JT and Liouville (super)gravity
• Boundary one-point function, Casimir energy and boundary state formalism in D+1 dimensional QFT
• Integrable quenches in the Hubbard model
• Exact solution of the one-dimensional super-symmetric t-J model with unparallel boundary fields
• Exact g-function flow between conformal field theories
• $Z_n$ elliptic Gaudin model with open boundaries
• On reflection algebras and twisted Yangians
• Boundary non-local charges from the open spin chain
• Boundary reduction formula
• Supersymmetry in the boundary tricritical Ising field theory
• Soliton-preserving boundary condition in affine Toda field theories
• Topological Kondo effect in star junctions of Ising magnetic chains. Exact solution
• Reflection-Transmission Quantum Yang-Baxter Equations
• Non-diagonal solutions of the reflection equation for the trigonometric $A_{n-1}^{(1)}$ vertex model
• Exact surface energy and helical spinons in the XXZ spin chain with arbitrary non-diagonal boundary fields
• Parity and Spin CFT with boundaries and defects
• Quantum many-body scars in spin models with multibody interactions
• Quantum fluctuation theorem in an interacting setup: point contacts in fractional quantum Hall edge state devices
• Direct Calculation of Breather S Matrices
• Introduction to Quantum Integrability
• Braiding of anyonic quasiparticles in the charge transfer statistics of symmetric fractional edge-state Mach-Zehnder interferometer
• Algebraic Bethe ansatz for the six vertex model with upper triangular $K$-matrices
• Achiral boundaries and the twisted Yangian of the D5-brane
• g-Functions and gluon scattering amplitudes at strong coupling
• Full counting statistics of chiral Luttinger liquids with impurities
• Yang-Baxter equation and reflection equations in integrable models
• Y-system for Y=0 brane in planar AdS/CFT
• On quantum group symmetry and Bethe ansatz for the asymmetric twin spin chain with integrable boundary
• Asymptotic representations of augmented q-Onsager algebra and boundary K-operators related to Baxter Q-operators
• Perturbative post-quench overlaps in Quantum Field Theory
• Boundary Resonances in S = 1/2 Antiferromagnetic Chains under a Staggered Field
• Boundary finite size corrections for multiparticle states and planar AdS/CFT
• Koornwinder polynomials and the XXZ spin chain
• Form-factors computation of Friedel oscillations in Luttinger liquids
• Exact solution of the spin-s Heisenberg chain with generic non-diagonal boundaries
• Tunneling in quantum wires I: Exact solution of the spin isotropic case
• Simplified Calculation of Boundary S Matrices
• Fusion and Analytical Bethe Ansatz for the $A_{\n-1}^{(1)}$ Open Spin Chain
• Surface Tension of a Metal-Electrolyte Boundary: Exactly Solvable Model
• Rise and fall of Yu-Shiba-Rusinov bound-states in charge conserving $s$-wave one-dimensional superconductors
• Duality Relations for Overlaps of Integrable Boundary States in AdS/dCFT
• Spinorial R-matrix
• Transfer matrix spectrum for cyclic representations of the 6-vertex reflection algebra II
• Q-systems with boundary parameters
• Diagonalization of the Heun-Askey-Wilson operator, Leonard pairs and the algebraic Bethe ansatz
• The R-matrix bootstrap for the 2d O(N) bosonic model with a boundary
• Strong coupling resistivity in the Kondo model
• Form factors in the presence of integrable defects
• The Scattering Theory of Oscillator Defects in an Optical Fiber
• Finite size effects in the spin-1 XXZ and supersymmetric sine-Gordon models with Dirichlet boundary conditions
• Local density of states of 1D Mott insulators and CDW states with a boundary
• Interfaces and wetting transition on the half plane. Exact results from field theory
• Form factors of boundary exponential operators in the sinh-Gordon model
• Coulomb Gas on the Half Plane
• Sinh-Gordon Boundary TBA and Boundary Liouville Reflection Amplitude
• Boundary Lax pairs for the $A_n^{(1)}$ Toda field theories
• Reflection Matrices for Integrable $N=1$ Supersymmetric Theories
• Surface Critical Phenomena and Scaling in the Eight-Vertex Model
• Exact diagonalization of the generalized supersymmetric t-J model with boundaries
• $A_{n-1}^{(1)}$ Reflection K-Matrices
• Null-polygonal minimal surfaces in AdS_4 from perturbed W minimal models
• Folding defect affine Toda field theories
• Reversible Fluxon Logic with optimized CNOT gate components
• Exact boundary free energy of the open XXZ chain with arbitrary boundary conditions
• Exact solution of the XXX Gaudin model with the generic open boundaries
• Bethe ansatz for an AdS/CFT open spin chain with non-diagonal boundaries
• Multiple phases and vicious walkers in a wedge
• A note on the boundary spin $s$ XXZ chain
• Boundary conditions changing operators in non conformal theories
• Multiple reference states and complete spectrum of the $Z_n$ Belavin model with open boundaries
• Exact solution of the supersymmetric sinh-Gordon model with boundary
• The scaling supersymmetric Yang-Lee model with boundary
• Reduced density matrix and entanglement in interacting quantum field theory with Hamiltonian truncation
• String integrability of the ABJM defect
• Casimir force between planes as a boundary finite size effect
• Integrable boundary interaction in 3D target space: the "pillow-brane" model
• Exact Partition Function and Boundary State of 2-D Massive Ising Field Theory with Boundary Magnetic Field
• Background field boundary conditions for affine Toda field theories
• Boundary breathers in the sinh-Gordon model
• Entanglement entropy and boundary renormalization group flow - exact results in the Ising universality class
• Boundary Action of N=2 Super-Liouville Theory
• Exact g-function flows from the staircase model
• Solving the quantum non-linear Schrodinger equation with delta-type impurity
• Tunneling in quantum wires II: A new line of IR fixed points
• The Super-Liouville-Equation on the Half-Line
• Boundary effects on the local density of states of one-dimensional Mott insulators and charge density wave states
• Boundary transfer matrices and boundary quantum KZ equations
• A study of truncation effects in boundary flows of the Ising model on a strip
• Surveying the quantum group symmetries of integrable open spin chains
• Extreme diagonally and antidiagonally symmetric alternating sign matrices of odd order
• Integrable Wilson loops in ABJM: a $Y$-system computation of the cusp anomalous dimension
• Quantum quenches in integrable systems: Constraints from factorisation
• Functional Equations and Separation of Variables for Exact g-Function
• The XXX spin s quantum chain and the alternating $s^1$, $s^2$ chain with boundaries
• Thermodynamic Bethe Ansatz for boundary sine-Gordon model
• Issues on magnon reflection
• Boundary form factors of the sinh-Gordon model with Dirichlet boundary conditions at the self-dual point
• Trigonometric sl(2) Gaudin model with boundary terms
• The integrable quantum group invariant A_{2n-1}^(2) and D_{n+1}^(2) open spin chains
• Soliton S matrices for the critical A_{N-1}^(1) chain
• Diagonalization of transfer matrix of supersymmetry $u_q(\widehat{sl}(m+1|n+1))$ chain with a boundary
• TBA boundary flows in the tricritical Ising field theory
• Determinant representations for scalar products of the XXZ Gaudin model with general boundary terms
• Exact Boundary Modes in an Interacting Quantum Wire
• D-branes in $\lambda$-deformations
• Edge Modes in One Dimensional Topological Charge Conserving Spin-Triplet Superconductors: Exact Results from Bethe Ansatz
• Breather boundary form factors in sine-Gordon theory
• Transmission through a potential barrier in Luttinger liquids with a topological spin gap
• Semiclassical Energy Levels of Sine-Gordon Model on a Strip with Dirichlet Boundary Conditions
• On Separation of Variables for Reflection Algebras
• A non-integrable quench from AdS/dCFT
• Correlation and entanglement spreading in nested spin chains
• The complex sine-Gordon model on a half line
• Quantum corrections to the classical reflection factor in A2(1) Toda Field Theory
• Multiparameter Integrable QFT's with N bosons
• Universality at work -- the local sine-Gordon model, lattice fermions, and quantum circuits
• Dynamical response functions in the quantum Ising chain with a boundary
• $A_n^{(1)}$ affine Toda field theories with integrable boundary conditions revisited
• Exactly solvable many-body dynamics from space-time duality
• Particles, conformal invariance and criticality in pure and disordered systems
• Quantum impurity approach to a coupled qubit problem
• Complete Nondiagonal Reflection Matrices of RSOS/SOS and Hard Hexagon Models
• Integrable supersymmetric correlated electron chain with open boundaries
• Signatures of Topological Superconductivity and Parafermion Zero Modes in Fractional Quantum Hall Edges
• The 1999 Heineman Prize Address- Integrable models in statistical mechanics: The hidden field with unsolved problems
• Bulk and boundary effects on the decay of the thermodynamic Casimir force
• Slowly decaying zero mode in a weakly non-integrable boundary impurity model
• Eigenstates of the Atom-Field Interaction and the Binding of Light in Photonic Crystals
• Inelastic decay from integrability
• Nonstandard coproducts and the Izergin-Korepin open spin chain
• Algebraic Bethe ansatz for the XXZ Heisenberg spin chain with triangular boundaries and the corresponding Gaudin model
• Classification of Solutions to Reflection Equation of Two-Component Systems
• Interface in presence of a wall. Results from field theory
• A geometric approach to free variable loop equations in discretized theories of 2D gravity
• Determinant representations of scalar products for the open XXZ chain with non-diagonal boundary terms
• Quantization of the Nonlinear Schrodinger Equation on the Half Line
• Supersymmetric Sine-Gordon Model and the Eight-Vertex Free Fermion model with Boundary
• Interface localization near criticality
• Form factors of boundary fields for A(2)-affine Toda field theory
• Bulk perturbations of N=2 branes
• The boundary N=2 supersymmetric sine-Gordon model
• Partition function of the trigonometric SOS model with reflecting end
• Finite temperature expectation values of boundary operators
• Multipoint correlation functions at phase separation. Exact results from field theory
• Generalized T-Q relations and the open XXZ chain
• Irrelevant Deformations with Boundaries and Defects
• New D_{n+1}^(2) K-matrices with quantum group symmetry
• Spectrum of local boundary operators from boundary form factor bootstrap
• A supersymmetric U_{q}[osp(2|2)]-extended Hubbard model with boundary fields
• Heisenberg XYZ Hamiltonian with Integrable Impurities
• Kink-boundary collisions in a two dimensional scalar field theory
• Form factors of the half-infinite XXZ spin chain with a triangular boundary
• Drinfeld twists of the open XXZ chain with non-diagonal boundary terms
• Boundary energy of the open XXX chain with a non-diagonal boundary term
• Correlation functions for open XXZ spin 1/2 quantum chains with unparallel boundary magnetic fields
• Jordanian deformation of the open XXX-spin chain
• Boundary S-matrix for the Integrable q-Potts Model
• Boundary Quantum Field Theories with Infinite Resonance States
• Universal Baxter TQ-relations for open boundary quantum integrable systems
• Existence of Low-Temperature Critical Regime in 1D Luttinger Liquid with a Weak Link
• Quantum Integrability of Certain Boundary Conditions
• Boundary S matrices with N=2 supersymmetry
• Crossing probability and number of crossing clusters in off-critical percolation
• Classical impurities and boundary Majorana zero modes in quantum chains
• On the Integrable Structure of the Ising Model
• Interplay between Zamolodchikov-Faddeev and Reflection-Transmission algebras
• The spectrum of quantum-group-invariant transfer matrices
• Holographic Weak Measurement
• The Ising model with a boundary magnetic field on a random surface
• Scalar product for the XXZ spin chain with general integrable boundaries
• Quantum fluctuations in one-dimensional supersolids
• (Semi)classical analysis of sine-Gordon theory on a strip
• Quench Dynamics in Two-Dimensional Integrable SUSY Models
• Boundary fields and renormalization group flow in the two-matrix model
• Integrable Crosscap States: From Spin Chains to 1D Bose Gas
• Tricritical Ising Model with a Boundary
• Quantum Theory of Self-Induced Transparency
• Fusion of SO(N) reflection matrices
• Boundary quantum Knizhnik-Zamolodchikov equations and Bethe vectors
• Revisiting the Y=0 open spin chain at one loop
• Classical Versus Quantum Symmetries for Toda Theories with a Nontrivial Boundary Perturbation
• Integral solutions to boundary quantum Knizhnik-Zamolodchikov equations
• On the effects of irrelevant boundary scaling operators
• Some semi-classical issues in boundary sine-Gordon model
• Boundary S Matrix for the XXZ Chain
• Determinant formula for the partition function of the six-vertex model with a non-diagonal reflecting end
• Splitting electrons into quasiparticles with fractional edge-state Mach-Zehnder interferometer
• The Massive Klein-Gordon Field Coupled to a Harmonic Oscillator at the Boundary
• Asymptotic safety in the sine-Gordon model
• Boundary Symmetry Breaking in CFT and the String Order Parameter
• Boundary versus bulk behavior of time-dependent correlation functions in one-dimensional quantum systems
• Statistics of charge transfer through impurities in strongly correlated 1D metals
• Boundary fermions and the plane wave
• On the ${\mathcal{U}}_q[sl(2)]$ Temperley-Lieb reflection matrices
• On boundary fusion and functional relations in the Baxterized affine Hecke algebra
• N=2 boundary supersymmetry in integrable models and perturbed boundary conformal field theory
• Measuring topological entanglement entropy using Maxwell relations
• Out-of-equilibrium transport in the interacting resonant level model: the surprising relevance of the boundary sine-Gordon model
• Fateev-Zamolodchikov and Kashiwara-Miwa models: boundary star-triangle relations and surface critical properties
• On integrable boundaries in the 2 dimensional $O(N)$ $\sigma$-models
• N=1 super sinh-Gordon model in the half line: Breather solutions
• The Kondo Model with a Bulk Mass Term
• On the Integrability of the Bukhvostov-Lipatov Model
• Planar quantum quenches: Computation of exact time-dependent correlation functions at large $N$
• Reflection algebra, Yangian symmetry and bound-states in AdS/CFT
• Local Magnetization in the Boundary Ising Chain at Finite Temperature
• Surface Critical Phenomena in Interaction-Round-a-Face Models
• Gaudin magnet with impurity and its generalized Knizhnik-Zamolodchikov equation
• Exactly solvable model of the 2D electrical double layer
• Boundary One-Point Functions, Scattering Theory and Vacuum Solutions in Integrable Systems
• Infinite dimension reflection matrices in the sine-Gordon model with a boundary
• Charge transfer statistics in symmetric fractional edge-state Mach-Zehnder interferometer
• Reflection Amplitudes of Boundary Toda Theories and Thermodynamic Bethe Ansatz
• Reflection Scattering Matrix of the Ising Model in a Random Boundary Magnetic Field
• Generalized T-Q relations and the open spin-s XXZ chain with nondiagonal boundary terms
• Integrable crosscaps in classical sigma models
• Behavior of Boundary String Field Theory Associated with Integrable Massless Flow
• Surface energy and elementary excitations of the XXZ spin chain with arbitrary boundary fields
• Quantum Electronic Circuits for Multicritical Ising Models
• Critical Ising Model with Boundary Magnetic Field: RG Interface and Effective Hamiltonians
• Exact (d)->(+)&(-) boundary flow in the tricritical Ising model
• Ising model with a boundary magnetic field - an example of a boundary flow
• Scattering amplitudes in non-Fermi liquid systems
• How Irrelevant Operators affect the Determination of Fractional Charge
• Integrable boundaries for the q-Hahn process
• Quantum quenches from an excited state
• Quantum group symmetries and completeness for A_{2n}^(2) open spin chains
• Matrix product construction for Koornwinder polynomials and fluctuations of the current in the open ASEP
• The SU(n) invariant massive Thirring model with boundary reflection
• Boundary energy of the general open XXZ chain at roots of unity
• External voltage sources and Tunneling in quantum wires
• Dynamics of quantum discommensurations in the Frenkel-Kontorova chain
• Relaxation dynamics of integrable field theories after a global quantum quench
• Demystifying integrable QFTs in AdS: No-go theorems for higher-spin charges
• D5-brane boundary reflection factors
• Algebraic Bethe Ansatz for O(2N) sigma models with integrable diagonal boundaries
• On the complete-spectrum characterization of quantum integrable spin chains via the inhomogeneous T-Q relation
• Nested algebraic Bethe ansatz for open GL(N) spin chains with projected K-matrices
• Giant magnons and non-maximal giant gravitons
• Correlation functions of twist fields from Ward identities in the massive Dirac theory
• Friedel oscillations of Density of States in a one-dimensional Mott insulator and Incommensurate Charge Density Wave/Superconductor
• Central extension of the reflection equations and an analog of Miki's formula
• Local density of states of a quarter-filled one-dimensional Mott insulator with a boundary
• Generalized Landau-Lifshitz models on the interval
• Extended T-systems, Q matrices and T-Q relations for $s\ell (2)$ models at roots of unity
• Reflection matrices with $U_q[os{p}^{(2)}(2|2m)]$ symmetry
• Observation of spin-charge separation and boundary bound states via the local density of states
• Boundary K-matrices and the Lax pair for 1D open XYZ spin-chain
• On the perturbative expansion of boundary reflection factors of the supersymmetric sinh-Gordon model
• On asymptotic behaviour in truncated conformal space approach
• Universal boundary reflection amplitudes
• NLIE of Dirichlet sine-Gordon Model for Boundary Bound States
• Wronskian-type formula for inhomogeneous TQ-equations
• Boundary S-matrix for the Gross-Neveu Model
• Entanglement Properties of Boundary State and Thermalization
• Spontaneous symmetry breaking in the non-linear Schrodinger hierarchy with defect
• Correlations in Quantum Spin Systems from the Boundary Effect
• Spin correlation function in 2D statistical mechanics models with inhomogeneous line defects
• Quantum complex sine-Gordon model on a half line
• Integrable Four-Fermi Models with a Boundary and Boson-Fermion Duality
• Correlation functions of determinant operators in conformal fishnet theory
• Generic triangular solutions of the reflection equation: $U_q(\widehat{s{l}_2})$ case
• An inhomogeneous Lax representation for the Hirota equation
• Algebraic Bethe ansatz for the supersymmetric $t-J$ model with reflecting boundary conditions
• Bound States for a Magnetic Impurity in a Superconductor
• On the quantum reflection factor for the sinh-Gordon model with general boundary conditions
• On unitary time evolution out of equilibrium
• Integrable boundaries in AdS/CFT: revisiting the Z=0 giant graviton and D7-brane
• q-deformed Supersymmetric t-J Model with a Boundary
• Difference equations for correlation functions of $A_{n-1}^{(1)}$-face model with boundary reflection
• Boundary bootstrap principle in two-dimensional integrable quantum field theories
• Quantum anomalies in A^{(1)}_r Toda theories with defects
• Bethe ansatz solution of the ${\tau }_2$-model with arbitrary boundary fields
• Theoretical proposal to obtain strong Majorana evidence from scanning tunneling spectroscopy of a vortex with a dissipative environment
• Massless Boundary Sine-Gordon Model Coupled to External Fields
• The solution of an open XXZ chain with arbitrary spin revisited
• Explicit boundary form factors: the scaling Lee-Yang model
• Asymptotic Bethe ansatz of ABJM open spin chain from giant graviton
• Boundary scattering in the SU(N) principal chiral model on the half-line with conjugating boundary conditions
• On the logarithmic bipartite fidelity of the open XXZ spin chain at $\Delta =-1/2$
• Conductance of a Dissipative Quantum Dot: Nonequilibrium Crossover Near a Non-Fermi-Liquid Quantum Critical Point
• Spin chains with boundary inhomogeneities
• Quantum boundary currents for nonsimply-laced Toda theories
• Branes in the plane wave background with gauge field condensates
• TCSA and the finite volume boundary state
• Finite-size correction and bulk hole-excitations for special case of an open XXZ chain with nondiagonal boundary terms at roots of unity
• Exact effective action for fermions in one dimension with backscattering at a boundary
• Boundary conformal fields and Tomita--Takesaki theory
• Differential equation for local magnetization in the boundary Ising model
• N=1 Supersymmetric Boundary Bootstrap
• Conserved currents of the three-reggeon interaction
• Self-equilibration theorem in quantum-point contacts of interacting electrons: time-dependent quantum fluctuations of tunnel transport beyond the Levitov-Lesovik scattering approach
• Generic boundary scattering in the open XXZ chain
• On the elliptic sinh-Gordon equation with Durham boundary conditions
• Boundary Reflection Matrix for $D_4^{(1)}$ Affine Toda Field Theory
• A note on open-chain transfer matrices from q-deformed su(2|2) S-matrices
• First order quantum corrections to the classical reflection factor of the sinh-Gordon model
• Form factors of the SU(2) invariant massive Thirring model with boundary reflection
• Square Root Singularity in Boundary Reflection Matrix
• Aspects of classical backgrounds and scattering for affine Toda theory on a half-line
• Defects and Perturbation
• Continuous representations of scalar products of Bethe vectors
• Integrability of the N=2 boundary sine-Gordon model
• Boundary effects on the supersymmetric sine-Gordon model through light-cone lattice approach
• Entanglement Entropy in Integrable Field Theories with Line Defects I. Topological Defect
• Normalization of Off-shell Boundary State, g-function and Zeta Function Regularization
• Growth of Rényi Entropies in Interacting Integrable Models and the Breakdown of the Quasiparticle Picture
• Integrable Floquet QFT: Elasticity and factorization under periodic driving
• Fusion for AdS/CFT boundary S-matrices
• Gauge Invariance and the Critical Properties of Quantum Hall Plateaux Transitions
• On correlation functions for the open XXZ chain with non-longitudinal boundary fields : the case with a constraint
• Three-Point Functions in ABJM and Bethe Ansatz
• Exact non-equilibrium current from the partition function for impurity transport problems
• Second order quantum corrections to the classical reflection factor of the sinh-Gordon model
• Quantum group symmetry of integrable systems with or without boundary
• Boundary Quantum Field Theories Perturbed by $\mathrm{T}\bar{\mathrm{T}}$: Towards a Form Factor Program
• Massive ghost theories with a line of defects
• Bethe States of the integrable spin-s chain with generic open boundaries
• A note on the IR limit of the NLIEs of boundary supersymmetric sine-Gordon model
• Factorization in integrable systems with impurity
• B-type anomaly coefficients for the D3-D7 domain wall
• Non-diagonal reflection for the non-critical XXZ model
• On the NLIE of (inhomogeneous) open spin-1 XXZ chain with general integrable boundary terms
• Boundary S matrix of an open XXZ spin chain with nondiagonal boundary terms
• Quantum simulation of the microscopic to macroscopic crossover using superconducting quantum impurities
• Applications of quantum integrable systems
• The Quantum Hall Effect: Unified Scaling Theory and Quasi-particles at the Edge
• Spin-spin correlators on the $\beta$/${\beta }^{\star }$ boundaries in 2D Ising-like models: exact analysis through theory of block Toeplitz determinants
• Classically and Quantum Integrable Systems with Boundary
• Integrability in out-of-equilibrium systems
• Difference equations for the higher rank XXZ model with a boundary
• Entanglement Entropy in Integrable Field Theories with Line Defects II. Non-topological Defect
• Flag Integrable Models and Generalized Graded Algebras
• Casimir effect in the boundary state formalism
• Quantum quenches in the sinh-Gordon and Lieb-Liniger models
• Entanglement of Stationary States in the Presence of Unstable Quasiparticles
• Ising model in a boundary magnetic field with random discontinuities
• Universal TT- and TQ-relations via centrally extended q-Onsager algebra
• Integrable Impurity Model with Spin and Flavour: Model Inspired by Resonant Tunneling in Quantum Dot
• Bethe Ansatz and boundary energy of the open spin-1/2 XXZ chain
• Integrable Field Theories with Defects
• Plateaux Transitions from S-matrices based on SL(2,Z) Invariant Field Theories
• Supersymmetric WZW $\sigma$ Model on Full and Half Plane
• On the nonclassicality in quantum JT gravity
• Quantum-group-invariant $D_{n+1}^{(2)}$ models: Bethe ansatz and finite-size spectrum
• Boundary reflection matrices of massive ${\varphi }_{1,3}$-perturbed unitary minimal models
• Boundary states for a free boson defined on finite geometries
• Random Walk with a Boundary Line as a Free Massive Boson with a Defect Line
• Time Evolution of the Symmetry Resolved Entanglement Entropy after a Mass Quench
• A note on a boundary sine-Gordon model at the free-Fermion point
• Spin-$s$ $Q$-systems: Twist and Open Boundaries
• Chiral Integrable Boundary States in the SU(4) Alternating Spin Chain
• Toda Lattice Models with Boundary
• Time evolution of effective central charge and signatures of RG irreversibility after a quantum quench
• The continuum limit of the integrable open XYZ spin-1/2 chain
• Steady state representations for the harmonic process
• NLIE and finite size effects of the spin-1/2 XXZ and sine-Gordon models with two boundaries revisited
• Boundary bound states and integrable Wilson loops in ABJM