Yang-Baxter equation in spin chains with long range interactions

Abstract

We consider the $su(n)$ spin chains with long range interactions and the spin generalization of the Calogero-Sutherland models. We show that their properties derive from a transfer matrix obeying the Yang-Baxter equation. We obtain the expression of the conserved quantities and we diagonalize them.

Saclay-t93/006

References in corpus (4)

• Exchange Operator Formalism for Integrable Systems of Particles
• Explicit Solution to the N-Body Calogero Problem
• On Models with Inverse-Square Exchange
• Invariants of the Haldane-Shastry $SU(N)$ Chain

Cited by in corpus (172)

• Fractional Quantum Hall States and Jack Polynomials
• Remarks on the notion of quantum integrability
• Physics and Mathematics of Calogero particles
• A Quasi-Hopf algebra interpretation of quantum 3-j and 6-j symbols and difference equations
• Excited States of Calogero-Sutherland Model and Singular Vectors of the $W_N$ Algebra
• The Yangian symmetry of the Hubbard Model
• A systematic construction of completely integrable Hamiltonians from coalgebras
• Dynamical correlation functions in the Calogero-Sutherland model
• Spinons in Conformal Field Theory
• Common Algebraic Structure for the Calogero-Sutherland Models
• The Calogero-Sutherland Model and Polynomials with Prescribed Symmetry
• Exact Solution of Long-Range Interacting Spin Chains with Boundaries
• The Gervais-Neveu-Felder equation and the quantum Calogero-Moser systems
• Spinon basis for higher level SU(2) WZW models
• Exclusion Statistics in Conformal Field Theory -- generalized fermions and spinons for level-1 WZW theories
• Conformal blocks in Virasoro and W theories: duality and the Calogero-Sutherland model
• Global properties of the spectrum of the Haldane-Shastry spin chain
• The SU(n)_1 WZW Models: Spinon Decomposition and Yangian Structure
• Yangian of the Queer Lie Superalgebra
• Exact Yangian Symmetry in the Classical Euler-Calogero-Moser Model
• Supersymmetric Calogero-Moser-Sutherland models and Jack superpolynomials
• Integral Representations of the Macdonald Symmetric Functions
• Rodrigues Formula for Hi-Jack Symmetric Polynomials Associated with the Quantum Calogero Model
• Multicomponent Calogero Model of $B_N$-Type Confined in Harmonic Potential
• Exact partition function of SU(m|n) supersymmetric Haldane-Shastry spin chain
• Form factors and generalized hydrodynamics for integrable systems
• Exact Solution of the Sutherland Model with arbitrary symmetry
• Haldane-Shastry spin chains of BC_N type
• Cuboctahedric Higgs oscillator from the Calogero model
• Bases in coset conformal field theory from AGT correspondence and Macdonald polynomials at the roots of unity
• Fixing the Quantum Three-Point Function
• A_N-type Dunkl operators and new spin Calogero-Sutherland models
• The Yangian Symmetry of the Hubbard Models with Variable Range Hopping
• Skew Young diagram method in spectral decomposition of integrable lattice models
• Integrable $1/r^2$ Spin Chain with Reflecting End
• Drinfeld Functor and Finite-Dimensional Representations of Yangian
• Integrals of motion of the Haldane Shastry Model
• Low energy properties of the SU(m|n) supersymmetric Haldane-Shastry spin chain
• On polynomials interpolating between the stationary state of a O(n) model and a Q.H.E. ground state
• New spin Calogero-Sutherland models related to B_N-type Dunkl operators
• Exact spectrum and partition function of SU(m|n) supersymmetric Polychronakos model
• Infinite Matrix Product States for long range SU(N) spin models
• Universal description of dissipative Tomonaga-Luttinger liquids with SU($N$) spin symmetry: Exact spectrum and critical exponents
• Yangian Symmetry and Quantum Inverse Scattering Method for the One-Dimensional Hubbard Model
• The Polychronakos-Frahm spin chain of BC_N type and Berry-Tabor's conjecture
• The orthogonal eigenbasis and norms of eigenvectors in the Spin Calogero-Sutherland Model
• A Note on Dressed S-Matrices in Models with Long-Range Interactions
• A note on the eigenvectors of long-range spin chains and their scalar products
• Exactly solvable D_N-type quantum spin models with long-range interaction
• Collective field theory of the matrix-vector model
• Spin-Singlet Quantum Hall States and Jack Polynomials with a Prescribed Symmetry
• Yangians, finite W-algebras and the Non Linear Schrodinger hierarchy
• Yangian symmetry in the Non Linear Schrodinger hierarchy
• Generalized isotropic Lipkin-Meshkov-Glick models: ground state entanglement and quantum entropies
• Spin dependent extension of Calogero-Sutherland model through anyon like representations of permutation operators
• Boson-fermion duality in SU(m|n) supersymmetric Haldane-Shastry spin chain
• Evaluation and normalization of Jack superpolynomials
• Quantum Lax pairs via Dunkl and Cherednik operators
• An exactly solvable supersymmetric spin chain of BC_N type
• Symmetries and exact solutions of some integrable Haldane-Shastry like spin chains
• Generalized Hermite polynomials in superspace as eigenfunctions of the supersymmetric rational CMS model
• Free harmonic oscillators, Jack polynomials and Calogero-Sutherland systems
• Inozemtsev's hyperbolic spin model and its related spin chain
• Notes on Collective Field Theory of Matrix and Spin Calogero Models
• On the Sutherland Spin Model of B_N Type and its Associated Spin Chain
• Resurrecting the partially isotropic Haldane-Shastry model
• On Hamiltonian structure of the spin Ruijsenaars-Schneider model
• BPS Operators in N=4 SYM: Calogero Models and 2D Fermions
• Thermodynamics of spin chains of Haldane-Shastry type and one-dimensional vertex models
• Algebraic Solution of the Hubbard Model on the Infinite Interval
• On R-matrix valued Lax pairs for Calogero-Moser models
• Solitons in a continuous classical Haldane-Shastry spin chain
• Exact Dynamics of the SU(K) Haldane-Shastry Model
• Algebra of one-particle operators for the Calogero model
• Hermite and Laguerre Symmetric Functions Associated with Operators of Calogero-Moser-Sutherland Type
• $gl(n|m)$ color Calogero-Sutherland models and Super Yangian Algebra
• Relativistic Calogero-Sutherland Model: Spin Generalization, Quantum Affine Symmetry and Dynamical Correlation Functions
• Yangian-invariant spin models and Fibonacci numbers
• Spin-Ruijsenaars, q-deformed Haldane-Shastry and Macdonald polynomials
• Spectral properties of supersymmetric Polychronakos spin chain associated with A_{N-1} root system
• Level-0 structure of level-1 $U_q({\widehat{sl}}_2)$-modules and Macdonald polynomials
• Dynamical Correlation Functions and Finite-size Scaling in Ruijsenaars-Schneider Model
• Yangian-invariant field theory of matrix-vector models
• Spherical Hecke algebra in the Nekrasov-Shatashvili limit
• The spin Sutherland model of D_N type and its associated spin chain
• The Classical $r$-Matrix for the Relativistic Ruijsenaars-Schneider System
• Universal Lax pairs for Spin Calogero-Moser Models and Spin Exchange Models
• Collective Field Description of Spin Calogero-Sutherland Models
• Observable algebra for the rational and trigonometric Euler Calogero Moser models
• Integrable N-particle Hamiltonians with Yangian or Reflection Algebra Symmetry
• The exactly solvable spin Sutherland model of B_N type and its related spin chain
• Integrable open spin chains related to infinite matrix product states
• Anisotropic spin generalization of elliptic Macdonald-Ruijsenaars operators and R-matrix identities
• One-Dimensional Vertex Models Associated with a Class of Yangian Invariant Haldane-Shastry Like Spin Chains
• Thermodynamics and criticality of supersymmetric spin chains with long-range interactions
• New Non-Symmetric Orthogonal Basis for the Calogero Model with Distinguishable Particles
• Semi-infinite wedges and the conformal limit of the fermionic Calogero-Sutherland Model with spin $\frac{1}{2}$
• Some Properties of the Calogero-Sutherland Model with Reflections
• Gaudin functions, and Euler-Poincaré characteristics
• Elliptic generalization of integrable q-deformed anisotropic Haldane-Shastry long-range spin chain
• Rodrigues Formula for the Nonsymmetric Multivariable Hermite Polynomial
• Integrable Models From Twisted Half Loop Algebras
• Multi-parameter deformed and nonstandard $Y(g{l}_M)$ Yangian symmetry in a novel class of spin Calogero-Sutherland models
• A lecture on the Calogero-Sutherland models
• On Spin Calogero-Moser system at infinity
• Rodrigues Formula for the Nonsymmetric Multivariable Laguerre Polynomial
• Higher Charges in Dynamical Spin Chains for SYM Theory
• Finite-difference representations of the degenerate affine Hecke algebra
• Exchange operator formalism for N-body spin models with near-neighbors interactions
• Symmetry protected topological phases beyond groups: The q-deformed bilinear-biquadratic spin chain
• Jack superpolynomials with negative fractional parameter: clustering properties and super-Virasoro ideals
• From fermionic spin-Calogero-Sutherland models to the Haldane-Shastry chain by freezing
• Level density distribution for one-dimensional vertex models related to Haldane-Shastry like spin chains
• Symmetric functions and the Yangian decomposition of the Fock and Basic modules of the affine Lie algebra \hat{sl(N)}
• The Yangian Symmetry in the Spin Calogero Model and its Applications
• Long Range Interaction Models and Yangian Symmetry
• Fusion, mass, and representation theory of the Yangian algebra
• Dunkl symplectic algebra in generalized Calogero models
• How coordinate Bethe ansatz works for Inozemtsev model
• Intertwining Operators for a Degenerate Double Affine Hecke Algebra and Multivariable Orthogonal Polynomials
• Yangian Symmetries in the $SU(N{)}_1$ WZW Model and the Calogero-Sutherland Model
• New integrable extension of the Hubbard chain with variable range hopping
• On the spectrum of S=1/2 XXX Heisenberg chain with elliptic exchange
• Knizhnik-Zamolodchikov equations and the Calogero-Sutherland-Moser integrable models with exchange terms
• Conserved charges of non-yangian type for the Frahm-Polychronakos spin chain
• Braid Structure and Raising-Lowering Operator Formalism in Sutherland Model
• A novel quasi-exactly solvable spin chain with nearest-neighbors interactions
• Partition functions of Polychronakos like spin chains associated with polarized spin reversal operators
• The Algebraic Structure of the $gl(n|m)$ Color Calogero-Sutherland Models
• Sutherland Models for Complex Reflection Groups
• Many-spinon states and representations of Yangians in the SU(n) Haldane--Shastry model
• The deformed Inozemtsev spin chain
• Three-body generalization of the Sutherland model with internal degrees of freedom
• Symmetries of Spin Calogero Models
• Fermionic limit of the Calogero-Sutherland system
• Macdonald polynomials in superspace as eigenfunctions of commuting operators
• Appearance of branched motifs in the spectra of $B{C}_N$ type Polychronakos spin chains
• Supersymmetric analogue of BC_N type rational integrable models with polarized spin reversal operators
• Rational quantum integrable systems of D_N type with polarized spin reversal operators
• The open Haldane-Shastry chain: thermodynamics and criticality
• Exact solution of $D_N$ type quantum Calogero model through a mapping to free harmonic oscillators
• On the solutions of multicomponent generalizations of the Lam{é} equation
• On symmetries of generalized Calogero model and Polychronakos-Frahm chain
• Exactly solvable quantum impurity model with inverse-square interactions
• Graphical Calculus for the Double Affine Q-Dependent Braid Group
• A novel class of translationally invariant spin chains with long-range interactions
• Dunkl and Cherednik operators
• Deconfined quantum criticality and generalised exclusion statistics in a non-hermitian BCS model
• Super Yangian Double $DY(gl(1|1))$ and Its Gauss Decomposition
• Super Rogers-Szegö polynomials associated with $B{C}_N$ type of Polychronakos spin chains
• The Yang-Baxter paradox
• Thermodynamics and criticality of su($m$) spin chains of Haldane-Shastry type
• Bethe ansatz inside Calogero-Sutherland models
• A solvable non-unitary fermionic long-range model with extended symmetry
• On the ground-state properties of antiferromagnetic half-integer spin chains with long-range interactions
• Scattering matrices and affine Hecke algebras
• A Haldane-Shastry spin chain of BC_N type in a constant magnetic field
• Multi-parameter deformed and nonstandard $Y(g{l}_M)$ Yangian symmetry in integrable variants of Haldane-Shastry spin chain
• Particle Propagator of Spin Calogero-Sutherland Model
• Derivation of Green's Function of Spin Calogero-Sutherland Model by Uglov's Method
• Scalar Symmetries of the Hubbard Models with Variable Range Hopping
• Twisted Cherednik spectrum as a $q,t$-deformation
• Symmetry of $osp(m|n)$ spin Calogero-Sutherland models
• A non-symmetric Yang-Baxter algebra for the quantum nonlinear Schrödinger model (PhD Thesis)
• Matrix elements of vertex operators and fermionic limit of spin Calogero-Sutherland system
• A non-symmetric Yang-Baxter Algebra for the Quantum Nonlinear Schrödinger Model
• Generalization of a result of Matsuo and Cherednik to the Calogero-Sutherland- Moser integrable models with exchange terms
• Dynamical symmetries of the Calogero-Coulomb model
• The q-deformed Haldane-Shastry chain at q=i with even length
• Jack polynomials with prescribed symmetry and some of their clustering properties
• Y(so(5)) symmtry of the nonlinear Schr$\ddot{o}$dinger model with four-cmponents
• A spin-shift relation of the Ruijsenaars-Schneider Hamiltonian of type $C_n$