Analytical Bethe Ansatz for closed and open gl(n)-spin chains in any representation

Abstract

We present an "algebraic treatment" of the analytical Bethe Ansatz. For this purpose, we introduce abstract monodromy and transfer matrices which provide an algebraic framework for the analytical Bethe Ansatz. It allows us to deal with a generic gl(n)-spin chain possessing on each site an arbitrary gl(n)-representation. For open spin chains, we use the classification of the reflection matrices to treat all the diagonal boundary cases. As a result, we obtain the Bethe equations in their full generality for closed and open spin chains. The classifications of finite dimensional irreducible representations for the Yangian (closed spin chains) and for the reflection algebras (open spin chains) are directly linked to the calculation of the transfer matrix eigenvalues. As examples, we recover the usual closed and open spin chains, we treat the alternating spin chains and the closed spin chain with impurity.

References in corpus (36)

• The Bethe-Ansatz for N=4 Super Yang-Mills
• Boundary S-Matrix and Boundary State in Two-Dimensional Integrable Quantum Field Theory
• The N=4 SYM Integrable Super Spin Chain
• High energy QCD as a completely integrable model
• The susceptibility and excitation spectrum of (VO)${}_2$P${}_2$O${}_7$ in ladder and dimer chain models
• On the quantum inverse scattering problem
• Bethe Ansatz solution of the open XXZ chain with nondiagonal boundary terms
• Spin-spin correlation functions of the XXZ-1/2 Heisenberg chain in a magnetic field
• Boundary K-matrices for the XYZ, XXZ AND XXX spin chains
• Integrability in QCD and beyond
• Completeness of the Bethe Ansatz solution of the open XXZ chain with nondiagonal boundary terms
• Integrability and WKB solution of twist-three evolution equations
• Evolution equations for quark-gluon distributions in multi-color QCD and open spin chains
• Determinant Representations for Correlation Functions of Spin-1/2 XXX and XXZ Heisenberg Magnets
• Analytic Bethe Ansatz for Fundamental Representations of Yangians
• Massless Flows II: the exact S-matrix approach
• General boundary conditions for the sl(N) and sl(M|N) open spin chains
• Correlation functions of the XXZ spin-1/2 Heisenberg chain at the free fermion point from their multiple integral representations
• Representations of reflection algebras
• Coexistence of double alternating antiferromagnetic chains in (VO)_2P_2O_7 : NMR study
• Bulk and Boundary S Matrices for the SU(N) Chain
• Exact solution of the open Heisenberg chain with two impurities
• Finite-dimensional irreducible representations of twisted Yangians
• Spin Chains with Periodic Array of Impurities
• Sine-Gordon quantum field theory on the half-line with quantum boundary degrees of freedom
• Third-neighbor and other four-point correlation functions of spin-1/2 XXZ chain
• Hecke algebraic approach to the reflection equation for spin chains
• Spontaneous symmetry breaking in the gl(N)-NLS hierarchy on the half line
• Next Nearest-Neighbor Correlation Functions of the Spin-1/2 XXZ Chain at Critical Region
• New solutions to the Reflection Equation and the projecting method
• Non-diagonal solutions to reflection equations in $su(n)$ spin chains
• On integrable Hamiltonians for higher spin XXZ chain
• Quantum transfer matrices for discrete and continuous quasi-exactly solvable problems
• Open su(4)-invariant spin ladder with boundary defects
• The XXX spin s quantum chain and the alternating $s^1$, $s^2$ chain with boundaries
• From the quantum Jacobi-Trudi and Giambelli formula to a nonlinear integral equation for thermodynamics of the higher spin Heisenberg model

Cited by in corpus (28)

• Nested Bethe ansatz for "all" closed spin chains
• Eigenvectors of open XXZ and ASEP models for a class of non-diagonal boundary conditions
• Boundary states, overlaps, nesting and bootstrapping AdS/dCFT
• Transfer matrix spectrum for cyclic representations of the 6-vertex reflection algebra I
• Analytical Bethe Ansatz for closed and open gl(M|N) super-spin chains in arbitrary representations and for any Dynkin diagram
• DMRG simulations of SU(N) Heisenberg chains using standard Young tableaux: fundamental representation and comparison with finite-size Bethe ansatz
• Generalized coordinate Bethe ansatz for non diagonal boundaries
• Exact diagonalization of Heisenberg $SU(N)$ chains in the fully symmetric and antisymmetric representations
• Nested Bethe ansatz for `all' open spin chains with diagonal boundary conditions
• The open XXZ spin chain in the SoV framework: scalar product of separate states
• Transfer matrix spectrum for cyclic representations of the 6-vertex reflection algebra II
• Completeness of Wronskian Bethe equations for rational gl(m|n) spin chains
• On Separation of Variables for Reflection Algebras
• $A_n^{(1)}$ affine Toda field theories with integrable boundary conditions revisited
• Nested Bethe ansatz for Y(gl(n)) open spin chains with diagonal boundary conditions
• Spin chains from dynamical quadratic algebras
• Dynamic Lattice Supersymmetry in gl(n|m) Spin Chains
• Family of Commuting Operators for the Totally Asymmetric Exclusion Process
• Irreducibility criterion for a finite-dimensional highest weight representation of the sl(2) loop algebra and the dimensions of reducible representations
• A nested sequence of projectors (2): Multiparameter multistate statistical models, Hamiltonians, S-matrices
• Transmission matrices in gl(N) & U_q(gl(N)) quantum spin chains
• Thermodynamical limit of general gl(N) spin chains: vacuum state and densities
• Analytical Bethe ansatz in gl(N) spin chains
• The $SU(3)\supset SO(3)$ missing label problem and the analytical Bethe ansatz
• Scattering matrix for a general gl(2) spin chain
• Thermodynamical limit of general gl(N) spin chains II: Excited states and energies
• A new class ${\hat{o}}_N$ of statistical models: Transfer matrix eigenstates, chain Hamiltonians, factorizable $S$-matrix
• Counting Bethe States in Twisted Spin Chains