How Algebraic Bethe Ansatz works for integrable model
arXiv:hep-th/9605187
Abstract
I study the technique of Algebraic Bethe Ansatz for solving integrable models and show how it works in detail on the simplest example of spin 1/2 XXX magnetic chain. Several other models are treated more superficially, only the specific details are given. Several parameters, appearing in these generalizations: spin , anisotropy parameter $\ga$, shift $\om$ in the alternating chain, allow to include in our treatment most known examples of soliton theory, including relativistic model of Quantum Field Theory.
Les-Houches lectures, 59 pages, Latex
References in corpus (1)
Cited by in corpus (283)
- The Bethe-Ansatz for N=4 Super Yang-Mills
- The N=4 SYM Integrable Super Spin Chain
- The Complete One-Loop Dilatation Operator of N=4 Super Yang-Mills Theory
- Multi-spin string solutions in AdS_5 x S^5
- Supersymmetric vacua and Bethe ansatz
- The su(2|3) Dynamic Spin Chain
- Integrating Over Higgs Branches
- Stringing Spins and Spinning Strings
- Quantum integrability and supersymmetric vacua
- The ODE/IM Correspondence
- An introduction to integrable techniques for one-dimensional quantum systems
- Matching Higher Conserved Charges for Strings and Spins
- Strongly coupled quantum discrete Liouville theory. I: Algebraic approach and duality
- Gauge/string duality for QCD conformal operators
- Spinning strings and AdS/CFT duality
- Tailoring Three-Point Functions and Integrability
- Exact Form Factors in Integrable Quantum Field Theories: the Sine-Gordon Model
- Quantization of models with non-compact quantum group symmetry. Modular XXZ magnet and lattice sinh-Gordon model
- String hypothesis for the AdS_5 x S^5 mirror
- Logarithmic scaling in gauge/string correspondence
- Deformations of N=4 SYM and integrable spin chain models
- Spinning strings and integrable spin chains in the AdS/CFT correspondence
- One-point Functions in Defect CFT and Integrability
- A Shortcut to the Q-Operator
- Planar N=4 Gauge Theory and the Hubbard Model
- Renormalization of twist-three operators and integrable lattice models
- Algebraic Curve for the SO(6) sector of AdS/CFT
- Yang-Mills Duals for Semiclassical Strings
- Large spin limits of AdS/CFT and generalized Landau-Lifshitz equations
- Small deformations of supersymmetric Wilson loops and open spin-chains
- Worldsheet Scattering in AdS_5 x S^5
- Quasilocal conservation laws in XXZ spin-1/2 chains: open, periodic and twisted boundary conditions
- Matrix product solutions of boundary driven quantum chains
- Antiperiodic spin-1/2 XXZ quantum chains by separation of variables: Complete spectrum and form factors
- One-point Functions in AdS/dCFT from Matrix Product States
- Correlation functions and transport coefficients in generalised hydrodynamics
- The Physicist's Companion to Current Fluctuations: One-Dimensional Bulk-Driven Lattice Gases
- Baxter Q-Operators and Representations of Yangians
- Non-diagonal open spin-1/2 XXZ quantum chains by separation of variables: Complete spectrum and matrix elements of some quasi-local operators
- Integrability and WKB solution of twist-three evolution equations
- Quantum corrections to spinning strings in AdS(5)xS(5) and Bethe ansatz: a comparative study
- Complete 1-loop test of AdS/CFT
- Yang-Mills Correlation Functions from Integrable Spin Chains
- Nested Bethe ansatz for "all" closed spin chains
- On the completeness of solutions of Bethe's equations
- Wrapping interactions and the genus expansion of the 2-point function of composite operators
- Quantum spectral curve as a tool for a perturbative quantum field theory
- 5D partition functions, q-Virasoro systems and integrable spin-chains
- Lectures on Yangian Symmetry
- Strong coupling limit of Bethe Ansatz equations
- Kardar-Parisi-Zhang physics in integrable rotationally symmetric dynamics on discrete space-time lattice
- Bethe Ansatz in Stringy Sigma Models
- On the Bethe Ansatz for the Jaynes-Cummings-Gaudin model
- Lectures on the Bethe Ansatz
- Integrable approach to simple exclusion processes with boundaries. Review and progress
- New Integrable Structures in Large-N QCD
- Integrability of the AdS_5 x S^5 superstring and its deformations
- Conformal algebra: R-matrix and star-triangle relation
- Higgs Bundles, Gauge Theories and Quantum Groups
- One-Loop QCD Spin Chain and its Spectrum
- Six-Vertex, Loop and Tiling models: Integrability and Combinatorics
- Modular Double of Quantum Group
- The Quantum Deformed Mirror TBA I
- On the Integrability of large N Plane-Wave Matrix Theory
- Pulsating Strings on AdS_5 x S^5
- N-Impurity Superstring Spectra Near the pp-Wave Limit
- Yang-Baxter operators and scattering amplitudes in super-Yang-Mills theory
- Basso-Dixon Correlators in Two-Dimensional Fishnet CFT
- Algebraic Bethe ansatz for open XXX model with triangular boundary matrices
- Spectral Parameters for Scattering Amplitudes in N=4 Super Yang-Mills Theory
- Oscillator Construction of su(n|m) Q-Operators
- On-shell Diagrams, Graßmannians and Integrability for Form Factors
- Spectrum of Quantum Transfer Matrices via Classical Many-Body Systems
- Relativistic Classical Integrable Tops and Quantum R-matrices
- The spectral problem for strings on twisted AdS_5 x S^5
- Hydrodynamics in lattice models with continuous non-Abelian symmetries
- Quantum integrability and functional equations
- Algebraic Bethe ansatz for singular solutions
- Hydrodynamic projections and the emergence of linearised Euler equations in one-dimensional isolated systems
- Introduction to the thermodynamic Bethe ansatz
- Higher Conserved Charges and Integrability for Spinning Strings in AdS_5 x S^5
- 1/J corrections to semiclassical AdS/CFT states from quantum Landau-Lifshitz model
- Finite-Size Corrections to Anomalous Dimensions in N=4 SYM Theory
- Correlations and commuting transfer matrices in integrable unitary circuits
- On Yangian Symmetry in Planar N=4 SYM
- Integrable Spin Chain and Operator Mixing in N=1,2 Supersymmetric Theories
- Quantum mechanics of null polygonal Wilson loops
- Yangians, S-matrices and AdS/CFT
- Form factors and complete spectrum of XXX antiperiodic higher spin chains by quantum separation of variables
- Double Scaling and Finite Size Corrections in sl(2) Spin Chain
- Asymptotic Bethe Ansatz on the GKP vacuum as a defect spin chain: scattering, particles and minimal area Wilson loops
- Bethe Ansatz for Yangian Invariants: Towards Super Yang-Mills Scattering Amplitudes
- Integrability of two-loop dilatation operator in gauge theories
- GL(3)-Based Quantum Integrable Composite Models. II. Form Factors of Local Operators
- Permutation operators, entanglement entropy, and the XXZ spin chain in the limit Δ-> -1
- Scalar products in generalized models with SU(3)-symmetry
- Sine-Gordon form factors in finite volume
- The low-energy limit of AdS/CFT and its TBA
- Complete spectrum of quantum integrable lattice models associated to Y(gl(n)) by separation of variables
- R-Matrix and Baxter Q-Operators for the Noncompact SL(N,C) Invariant Spin Chain
- Algebraic Bethe Circuits
- Review of AdS/CFT Integrability, Chapter III.7: Hirota Dynamics for Quantum Integrability
- Spin bit models from non-planar N=4 SYM
- Bethe ansatz and fluctuations in SU(3) Yang-Mills operators
- Towards Baxter equation in supersymmetric Yang-Mills theories
- On the form factors of local operators in the Bazhanov-Stroganov and chiral Potts models
- Quantum string integrability and AdS/CFT
- The star-triangle relation and 3d superconformal indices
- Phantom Bethe excitations and spin helix eigenstates in integrable periodic and open spin chains
- Macdonald processes, quantum integrable systems and the Kardar-Parisi-Zhang universality class
- Instanton R-matrix and W-symmetry
- On the finite size corrections of anti-ferromagnetic anomalous dimensions in SYM
- Form factors of integrable Heisenberg (higher) spin chains
- Bethe Ansaetze for GKP strings
- Review of AdS/CFT Integrability, Chapter III.1: Bethe Ansätze and the R-Matrix Formalism
- First principle approach to correlation functions of spin-1/2 Heisenberg chain : fourth-neighbor correlators
- Singular solutions, repeated roots and completeness for higher-spin chains
- Antiferromagnetic Operators in N=4 Supersymmetric Yang-Mills Theory
- Open two-species exclusion processes with integrable boundaries
- QQ-system and Weyl-type transfer matrices in integrable SO(2r) spin chains
- Bound State Transfer Matrix for AdS5 x S5 Superstring
- Nested Bethe ansatz for `all' open spin chains with diagonal boundary conditions
- Spin Models and Superconformal Yang-Mills Theory
- A note on the eigenvectors of long-range spin chains and their scalar products
- Preparing exact eigenstates of the open XXZ chain on a quantum computer
- Diagonal Form Factors and Heavy-Heavy-Light Three-Point Functions at Weak Coupling
- Inner products in integrable Richardson-Gaudin models
- Integrable systems from the classical reflection equation
- Bethe Ansatz Equations for General Orbifolds of N=4 SYM
- From Polygon Wilson Loops to Spin Chains and Back
- On Generalized -systems
- Yangian symmetric correlators
- Lattice Super Yang-Mills: A Virial Approach to Operator Dimensions
- On the anatomy of multi-spin magnon and single spike string solutions
- 6D SCFTs, 4D SCFTs, Conformal Matter, and Spin Chains
- Trigonometric osp(1|2) Gaudin model
- Crosscap States in Integrable Field Theories and Spin Chains
- Slow-string limit and "antiferromagnetic" state in AdS/CFT
- Integrability of the evolution equations for heavy-light baryon distribution amplitudes
- Conserved charges in the quantum simulation of integrable spin chains
- Bethe vectors for models based on the super-Yangian
- Q-operators for the open Heisenberg spin chain
- Quantum phase transitions in Bose-Einstein condensates from a Bethe ansatz perspective
- A supersymmetric matrix model: III. Hidden SUSY in statistical systems
- Strong coupling expansion of Baxter equation in N=4 SYM
- Bethe Ansatz and Bethe Vectors Scalar Products
- Asymptotic Four Point Functions
- Comments on World-Sheet Form Factors in AdS/CFT
- A review of the AdS/CFT Quantum Spectral Curve
- On Complex Gamma-Function Integrals
- The Quantum Yang Baxter conditions: The fundamental relations behind the Nambu-Goldstone theorem
- Baxter Q-operators of the XXZ chain and R-matrix factorization
- Algebraic Bethe ansatz for the XXX chain with triangular boundaries and Gaudin model
- Duality Relations for Overlaps of Integrable Boundary States in AdS/dCFT
- Hydrodynamic Equations for the Toda Lattice
- Baxter operators for arbitrary spin II
- Fusion Operators in the Generalized -model and Root-of-unity Symmetry of the XXZ Spin Chain of Higher Spin
- Quantum symmetry algebras of spin systems related to Temperley-Lieb R-matrices
- Mirror channel eigenvectors of the -dimensional fishnets
- The su(2|3) Undynamic Spin Chain
- Integrable Deformations of the XXZ Spin Chain
- Algebraic Bethe Ansatz approach to form factors and correlation functions of the cyclic eight-vertex solid-on-solid model
- Algebraic Quantization of Integrable Models in Discrete Space-time
- Aspects of Integrability in AdS/CFT Duality
- Exact solution of an integrable non-equilibrium particle system
- Qubit Construction in 6D SCFTs
- Reflection -matrices related to Temperley-Lieb -matrices
- On the multi-spin magnon and spike solutions from membranes
- Scalar products in models with GL(3) trigonometric R-matrix. Highest coefficient
- Orthogonal and symplectic Yangians and Yang-Baxter R-operators
- The Bethe Ansatz as a Quantum Circuit
- Bethe Ansatz Equations of XXZ Model and q-Sturm-Liouville Problems
- Staggered Anisotropy Parameter Modification of the Anisotropic Model
- Universal corrections to the entanglement entropy in gapped quantum spin chains: a numerical study
- Lifting asymptotic degeneracies with the Mirror TBA
- Integrable Spin Chains on the Conformal Moose
- Integrable Ladder t-J Model with Staggered Shift of the Spectral Parameter
- Toy models for wrapping effects
- Thermodynamics and conformal properties of XXZ chains with alternating spins
- Multiple commutation relations in the models with gl(2|1) symmetry
- Integrable strings for AdS/CFT
- Algebraic Bethe ansatz for the sl(2) Gaudin model with boundary
- The Gauge-Bethe Correspondence and Geometric Representation Theory
- Algebraic Bethe Ansatz for U(1) Invariant Integrable Models: The Method and General Results
- Quantum Anisotropic Sigma and Lambda Models as Spin Chains
- Integrable deformations of superintegrable quantum circuits
- Matrix Models, Complex Geometry and Integrable Systems. I
- Scalar Products in Twisted XXX Spin Chain. Determinant Representation
- The Floquet Baxterisation
- On string integrability. A journey through the two-dimensional hidden symmetries in the AdS/CFT dualities
- Integrable lattice spin models from supersymmetric dualities
- Algebraic Bethe ansatz for the XXZ Heisenberg spin chain with triangular boundaries and the corresponding Gaudin model
- Nested Bethe ansatz for Y(gl(n)) open spin chains with diagonal boundary conditions
- Gustafson Integrals
- Spinorial R operator and Algebraic Bethe Ansatz
- Hexagonalization of Fishnet integrals I: mirror excitations
- Spin bits at two loops
- The Transfer Matrix of Superintegrable Chiral Potts Model as the Q-operator of Root-of-unity XXZ Chain with Cyclic Representation of
- Yangians and Yang-Baxter R-operators for ortho-symplectic superalgebras
- Binary trees, coproducts, and integrable systems
- Coordinate Bethe Ansatz for Spin s XXX Model
- Integrable Models From Twisted Half Loop Algebras
- Integrable heat conduction model
- Integrable spin chains and cellular automata with medium range interaction
- Non-regular eigenstate of the XXX model as some limit of the Bethe state
- Yang-Baxter R-operators for osp superalgebras
- Bethe-State Counting and the Witten Index
- Integrability in Sigma-Models
- On the Integrability of String Theory in AdS_5 x S^5
- On the breakdown of perturbative integrability in large N matrix models
- A pedagogical introduction to quantum integrability, with a view towards theoretical high-energy physics
- Spin- Rational -system
- Exact Large Deviations of the Current in the Asymmetric Simple Exclusion Process with Open Boundaries
- Bethe ansatz and Hirota equation in integrable models
- Adiabatic gauge potential and integrability breaking with free fermions
- Notes on the Causal Structure in a Tensor Network
- X=M Theorem: Fermionic formulas and rigged configurations under review
- On the massless modes of the AdS3/CFT2 integrable systems
- On -model in Chiral Potts Model and Cyclic Representation of Quantum Group
- Giant Holes
- The completeness of the Bethe ansatz for the periodic ASEP
- The nineteen-vertex model and alternating sign matrices
- The hyperbolic modular double and the Yang-Baxter equation
- All correlation functions of the open XXX spin 1/2 quantum chains for unparallel boundary magnetic fields with one constraint
- Baxter Q-operators for integrable DST chain
- Free fermions in classical and quantum integrable models
- Rigged configurations and the Bethe Ansatz
- Bethe Vectors for Composite Models with and Supersymmetry
- Combinatorics of generalized Bethe equations
- QCD-like properties for anomalous dimensions in N=4 SYM
- Creation operators and algebraic Bethe ansatz for the elliptic quantum group
- Conformal quantum mechanics & the integrable spinning Fishnet
- Recurrence relations for off-shell Bethe vectors in trigonometric integrable models
- Thermodynamics of Inozemtsev's Elliptic Spin Chain
- Quantization of the N=2 Supersymmetric KdV Hierarchy
- Wrapping effects in supersymmetric gauge theories
- Effective Field Theory and Integrability in Two-Dimensional Mott Transition
- Boundary K-matrices and the Lax pair for 1D open XYZ spin-chain
- Algebraic Bethe ansatz for the Temperley-Lieb spin-1 chain
- Baxters's Q-operators for the simplest q-deformed model
- Thermodynamical limit of general gl(N) spin chains: vacuum state and densities
- On the Semi-Classical Limit of Scalar Products of the XXZ Spin Chain
- Rational Q-systems at Root of Unity I. Closed Chains
- Orthogonal and symplectic Yangians - linear and quadratic evaluations
- String Functions for Affine Lie Algebras Integrable Modules
- Boundary Perimeter Bethe Ansatz
- Quasilocal Conservation Laws in the Quantum Hirota Model
- Topologically Twisted SUSY Gauge Theory, Gauge-Bethe Correspondence and Quantum Cohomology
- Multiplicity A_m Models
- Jordanian deformation of the open sl(2) Gaudin model
- Solution of quantum integrable systems from quiver gauge theories
- Scattering matrix for a general gl(2) spin chain
- On scalar products and form factors by Separation of Variables: the antiperiodic XXZ model
- Overlap between usual and modified Bethe vectors
- Construction of the Bethe State for the Elliptic Quantum Group
- Osp(1|2) Off-shell Bethe Ansatz Equations
- A chain of strongly correlated SU(2)_4 anyons: Hamiltonian and Hilbert space of states
- Fractal decompositions and tensor network representations of Bethe wavefunctions
- On the structure of Bethe vectors
- General scalar products in the arbitrary six-vertex model
- Baxter's T-Q Relation and Bethe Ansatz of Discrete Quantum Pendulum and Sine-Gordon Model
- Bethe's Quantum Numbers And Rigged Configurations
- Baxterization of GL_q(2) and its application to the Liouville model and some other models on a lattice
- Anchoring and Binning the Coordinate Bethe Ansatz
- The scalar product of XXZ spin chain revisited. Application to the ground state at
- On one ansatz for sl_2-invariant R-matrices
- On the Algebraic Bethe Ansatz for XXX spin chain: creation operators "beyond the equator"
- On string solutions of Bethe equations in N=4 supersymmetric Yang-Mills theory
- On higher spin Uq(sl_2)-invariant R-matrices
- Bethe ansatz on a quantum computer?
- Factorization identities and algebraic Bethe ansatz for models
- Bethe vectors of the osp(1|2) Gaudin model
- Representations of orthogonal and symplectic Yangians
- On the Integrable Structure of Super Yang-Mills Scattering Amplitudes
- Classical Non-equilibrium Phases from a Quantum Perspective: Quasi-adiabatic evolution and Local Ansatz for Solving The Equilibrium State of Local Stochastic Dynamics
- Algebraic Bethe ansatz for Q-operators: The Heisenberg spin chain
- Q-operator for the quantum NLS model
- A diagrammatic approach towards the thermodynamics of integrable systems
- Spin- -systems: Twist and Open Boundaries
- Momentum Evolution Numerics of an Impurity in a Quantum Quench
- All 4 x 4 solutions of the quantum Yang-Baxter equation
- Integrable fishnet circuits and Brownian solitons
- Bethe/Gauge correspodence: a short review on an aspect of the integrability nature of supersymmetric gauge theories