Deriving Boundary S Matrices

Abstract

We show how to derive exact boundary $S$ matrices for integrable quantum field theories in 1+1 dimensions using lattice regularization. We do this calculation explicitly for the sine-Gordon model with fixed boundary conditions using the Bethe ansatz for an XXZ-type spin chain in a boundary magnetic field. Our results agree with recent conjectures of Ghoshal and Zamolodchikov, and indicate that the only solutions to the Bethe equations which contribute to the scaling limit are the standard strings.

13 pages, USC-94-001

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Cited by in corpus (69)

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• Exact solution of a massless scalar field with a relevant boundary interaction
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• Integrable XYZ Spin Chain with Boundaries
• Correlation functions of the open XXZ chain I
• g-function flow in perturbed boundary conformal field theories
• Statistical Models with a Line of Defect
• Surface excitations and surface energy of the antiferromagnetic XXZ chain by the Bethe ansatz approach
• Bethe ansatz for the XXX-S chain with non-diagonal open boundaries
• Boundary bound states and boundary bootstrap in the sine-Gordon model with Dirichlet boundary conditions.
• Correlation functions of the open XXZ chain II
• The Supersymmetric t-J Model with a Boundary
• Algebraic Bethe ansatz for eight vertex model with general open-boundary conditions
• Boundary Exchange Algebras and Scattering on the Half Line
• Duality and quantum-algebra symmetry of the A_{N-1}^(1) open spin chain with diagonal boundary fields
• Spontaneous symmetry breaking in the gl(N)-NLS hierarchy on the half line
• The XX--model with boundaries. Part I: Diagonalization of the finite chain
• Anisotropic Spin-1/2 Heisenberg Chain with Open Boundary Conditions
• Fusion Hierarchy and Finite-Size Corrections of $U_q[sl(2)]$ Invariant Vertex Models with Open Boundaries
• Finite size effects in the XXZ and sine-Gordon models with two boundaries
• Bethe Ansatz solution of the open XX spin chain with nondiagonal boundary terms
• Violation of the string hypothesis and Heisenberg XXZ spin chain
• Loschmidt Amplitude and Work Distribution in Quenches of the Sine-Gordon Model
• Boundary states and finite size effects in sine-Gordon model with Neumann boundary condition
• On Generalized $Q$-systems
• Boundary form factors in finite volume
• The Bethe Ansatz Equations for Reflecting Magnons
• NLIE for hole excited states in the sine-Gordon model with two boundaries
• Direct Calculation of Breather S Matrices
• Delta-Bose gas on a half-line and the KPZ equation: boundary bound states and unbinding transitions
• Surface Tension of a Metal-Electrolyte Boundary: Exactly Solvable Model
• $T\overline{T}$ deformation in SCFTs and integrable supersymmetric theories
• Finite size effects in the spin-1 XXZ and supersymmetric sine-Gordon models with Dirichlet boundary conditions
• Exact Partition Function and Boundary State of Critical Ising Model with Boundary Magnetic Field
• Exact diagonalization of the generalized supersymmetric t-J model with boundaries
• The scaling supersymmetric Yang-Lee model with boundary
• Exact solution of the supersymmetric sinh-Gordon model with boundary
• Counting solutions of the Bethe equations of the quantum group invariant open XXZ chain at roots of unity
• A study of truncation effects in boundary flows of the Ising model on a strip
• TBA boundary flows in the tricritical Ising field theory
• Soliton S matrices for the critical A_{N-1}^(1) chain
• Bethe ansatz description of edge-localization in the open-boundary XXZ spin chain
• Universality at work -- the local sine-Gordon model, lattice fermions, and quantum circuits
• Exact Theory of Polymer Adsorption in Analogy with the Kondo Problem
• Breather boundary form factors in sine-Gordon theory
• Fermi gas with attractive potential and arbitrary spin in one-dimensional trap
• Finite temperature expectation values of boundary operators
• Boundary S-matrix for the Integrable q-Potts Model
• Heisenberg XYZ Hamiltonian with Integrable Impurities
• Boundary S Matrix for the XXZ Chain
• Estimating Bethe roots with VQE
• Surface energy and elementary excitations of the XXZ spin chain with arbitrary boundary fields
• Thermodynamic limit and boundary energy of the spin-1 Heisenberg chain with non-diagonal boundary fields
• Integrable Four-Fermi Models with a Boundary and Boson-Fermion Duality
• Algebraic Bethe ansatz for the supersymmetric $t-J$ model with reflecting boundary conditions
• Reflection Factors for the Principal Chiral Model
• Generic boundary scattering in the open XXZ chain
• Boundary TBA Equations for a Non-diagonal Theory
• Boundary effects on the supersymmetric sine-Gordon model through light-cone lattice approach
• Boundary S matrices for the open Hubbard chain with boundary fields
• Non-diagonal reflection for the non-critical XXZ model
• A note on the IR limit of the NLIEs of boundary supersymmetric sine-Gordon 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
• NLIE and finite size effects of the spin-1/2 XXZ and sine-Gordon models with two boundaries revisited
• Excitations and S-matrix for su(3) spin chain combining $3$ and ${3^{*}}
• Plateaux Transitions from S-matrices based on SL(2,Z) Invariant Field Theories
• Boundary reflection matrices of massive ${\varphi }_{1,3}$-perturbed unitary minimal models
• A note on a boundary sine-Gordon model at the free-Fermion point