Algebraic Aspects of Bethe-Ansatz

Abstract

In these lectures the introduction to algebraic aspects of Bethe Ansatz is given. The applications to the seminal spin 1/2 XXX model is discussed in detail and the generalization to higher spin as well as XXZ and lattice Sine-Gordon model are indicated. The origin of quantum groups and their appearance in CFT models is explained. The text can be considered as a guide to the research papers in this field.

(Lectures delivered by L. D. Faddeev at the Institute for Theoretical Physics, SUNY at Stony Brook, lecture notes written by Kostas Skenderis), 42 pages, ITP-SB-94-11, Latex

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• Logarithmic scaling in gauge/string correspondence
• Noncompact Heisenberg spin magnets from high-energy QCD: I. Baxter Q-operator and Separation of Variables
• Algebraic Bethe ansatz method for the exact calculation of energy spectra and form factors: applications to models of Bose-Einstein condensates and metallic nanograins
• Renormalization of twist-three operators and integrable lattice models
• Supersymmetric Bethe Ansatz and Baxter Equations from Discrete Hirota Dynamics
• Evolution equations for quark-gluon distributions in multi-color QCD and open spin chains
• Holographic quantum algorithms for simulating correlated spin systems
• Developments in the Tensor Network -- from Statistical Mechanics to Quantum Entanglement
• Form factor expansion for thermal correlators
• Exactly conserved quasilocal operators for the XXZ spin chain
• Baxter Q-operator and Separation of Variables for the open SL(2,R) spin chain
• Separation of variables for the quantum SL(2,R) spin chain
• Quantum and classical integrable sine-Gordon model with defect
• Quantum Group Representations and Baxter Equation
• Pumping approximately integrable systems
• Classical tau-function for quantum spin chains
• Noncompact Heisenberg spin magnets from high-energy QCD: II. Quantization conditions and energy spectrum
• Backlund transformations for difference Hirota equation and supersymmetric Bethe ansatz
• Excited state correlations of the finite Heisenberg chain
• Bethe Ansatz for Yangian Invariants: Towards Super Yang-Mills Scattering Amplitudes
• Integrability of two-loop dilatation operator in gauge theories
• Integrability and exact spectrum of a pairing model for nucleons
• Phase Diagram of the Heisenberg Spin Ladder with Ring Exchange
• Towards Baxter equation in supersymmetric Yang-Mills theories
• Algebraic Bethe Ansatz for the two species ASEP with different hopping rates
• Entanglement entropy production in deep inelastic scattering
• Review of AdS/CFT Integrability, Chapter III.1: Bethe Ansätze and the R-Matrix Formalism
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• Integrability of the russian doll BCS model
• Spin Models and Superconformal Yang-Mills Theory
• Algebraic approach in unifying quantum integrable models
• Spin dependent extension of Calogero-Sutherland model through anyon like representations of permutation operators
• Quantum and Classical Integrable Systems
• Noncompact SL(2,R) spin chain
• Strong coupling expansion of Baxter equation in N=4 SYM
• Shape changing and accelerating solitons in integrable variable mass sine-Gordon model
• Fermionic R-Operator for the Fermion Chain Model
• LATTICE CONFORMAL THEORIES AND THEIR INTEGRABLE PERTURBATIONS
• Quantum group approach to steady states of boundary-driven open quantum systems
• On the Correspondence Between the Strongly Coupled 2-Flavor Lattice Schwinger Model and the Heisenberg Antiferromagnetic Chain
• On the partition function of the six-vertex model with domain wall boundary conditions
• Introduction to Quantum Integrability
• Multipartite entanglement in the 1-D spin-$\frac{1}{2}$ Heisenberg Antiferromagnet
• Quantum integrable multi-well tunneling models
• Integrability breaking in the one dimensional Bose gas: Atomic losses and energy loss
• Noncompact Heisenberg spin magnets from high-energy QCD: III. Quasiclassical approach
• Integrable strings for AdS/CFT
• Exact solution to the Schrodinger's equation with pseudo-Gaussian potential
• An Algebraic Bootstrap for Dimensionally Reduced Quantum Gravity
• Popcorn Drude weights from quantum symmetry
• Classification of Solutions to Reflection Equation of Two-Component Systems
• Statistical mechanics of integrable quantum spin systems
• Solvable models of Bose-Einstein condensates: a new algebraic Bethe ansatz scheme
• Dynamical Spin Chains in 4D $\mathcal{N}=2$ SCFTs
• The Quantum Algebraic Structure of the Twisted XXZ Chain
• Gauss hypergeometric function and quadratic R-matrix algebras
• Bethe ansatz and Hirota equation in integrable models
• Exactly soluble isotropic spin-1/2 ladder models
• Type-I integrable quantum impurities in the Heisenberg model
• Fundamental charges for dual-unitary circuits
• KPZ fluctuations in finite volume
• Integrable coupling in a model for Josephson tunneling between non-identical BCS systems
• Charge varying sine-Gordon deformed defects
• Duality for metaplectic ice
• Yang-Baxter algebra and generation of quantum integrable models
• Transmission amplitudes from Bethe ansatz equations
• Bethe states for the two-site Bose-Hubbard model: a binomial approach
• q-Boson in Quantum Integrable Systems
• A note on gl_N type-I integrable defects
• Violation of S-matrix factorization in massive Thirring model
• Exactly solvable dynamics and signatures of integrability in an infinite-range many-body Floquet spin system
• Transmission matrices in gl(N) & U_q(gl(N)) quantum spin chains
• The Role of the Central Element in the Quantum Algebra Underlying the Twisted XXZ Chain
• Reducing Circuit Depth in Quantum State Preparation for Quantum Simulation Using Measurements and Feedforward
• Exactly solvable models for multiatomic molecular Bose-Einstein condensates
• On the exactly solvable pairing models for bosons
• A bosonic multi-state two-well model
• New series of integrable vertex models through a unifying approach
• Exact solution at integrable coupling of a model for the Josephson effect between small metallic grains
• Solution of quantum integrable systems from quiver gauge theories
• Stochastic analysis & discrete quantum systems
• Signatures of Integrability and Exactly Solvable Dynamics in an Infinite-Range Many-Body Floquet Spin System
• Quantum walled Brauer algebra: commuting families, Baxterization, and representations
• On the tensor Permutation Matrices
• New Fundamental Symmetries of Integrable Systems and Partial Bethe Ansatz
• Exact Solvability Of Entanglement For Arbitrary Initial State in an Infinite-Range Floquet System
• A connection between $\mathcal{R}$-invariants and Yang-Baxter $R$-operators in $\mathcal{N}=4$ super-Yang-Mills theory
• Quasi-Exactly Solvable Deformations of Gaudin Models and ``Quasi-Gaudin Algebras''
• Bethe Ansatz for Heisenberg XXX Model
• Solitons in lattice field theories via tight-binding supersymmetry
• Rectangle Gell-Mann Matrices
• Algebraic construction of quantum integrable models including inhomogeneous models
• Sequential Bethe vectors and the quantum Ernst system