arXiv:cond-mat/9504096 · Journal of Physics A Mathematical and General

On the spectrum of S= 1/2 XXX Heisenberg chain with elliptic exchange

V I Inozemtsev

Published Aug 21, 1995• 5 citations

Abstract

It is found that the Hamiltonian of the S= 1/2 isotropic Heisenberg chain with N sites and elliptic non-nearest-neighbour exchange is diagonalized in each sector of the Hilbert space with magnetization N/2-M, 1<M<or=(N/2), by means of double quasiperiodic meromorphic solutions to the M-particle quantum Calogero-Moser problem on a line. The spectrum and highest-weight states are determined by the solutions of the systems of transcendental Bethe-ansatz-type equations which arise as restrictions on particle pseudomomenta.

DOI: 10.1088/0305-4470/28/16/004

Related papers

Bethe-ansatz equations for quantum Heisenberg chains with elliptic exchange

V. I. Inozemtsev

arXiv:math-ph/9911022Nov 17, 19992 citations

Solution to three-magnon problem for S=1/2 periodic quantum spin chains with elliptic exchange

V. I. Inozemtsev

The method of solving the three-particle quantum elliptic Calogero–Moser problem is applied to the description of three-magnon wave functions for the S=1/2 quantum Heisenberg chains with the exchange interaction given by the Weierstrass d function. The Bethe-like algebraic equations for the three-magnon case are presented in the explicit form.

Journal of Mathematical PhysicsJan 1, 19968 citations

The Extended Bethe Ansatz for Infinite S = 1/2 Quantum Spin Chains with Non-Nearest-Neighbor Interaction

V. I. lnozemtsev

Jan 1, 20050 citations

Exact solution of an S =1/2 Heisenberg antiferromagnetic chain with long-ranged interactions

B. Sriram Shastry

Physical Review LettersFeb 15, 1988769 citations

Integrable Heisenberg-van Vleck chains with variable range exchange

V. I. Inozemtsev

arXiv:hep-th/0201001Jan 1, 200232 citations

Bethe Ansatz for Heisenberg XXX Model

Shao-shiung Lin, Shi-shyr Roan

arXiv:cond-mat/9509183Oct 2, 19951 citation

arXiv:cond-mat/9504096 · Journal of Physics A Mathematical and General

On the spectrum of S= 1/2 XXX Heisenberg chain with elliptic exchange

V I Inozemtsev

Published Aug 21, 1995• 5 citations

arXiv HTML PDF

Abstract

DOI: 10.1088/0305-4470/28/16/004

Related papers

Bethe-ansatz equations for quantum Heisenberg chains with elliptic exchange

V. I. Inozemtsev

The eigenvectors of the Hamiltonian ${\cal H}_{N}$ of $N$ -sites quantum spin chains with elliptic exchange are connected with the double Bloch meromorphic solutions of the quantum continuous elliptic Calogero-Moser problem. This fact allows one to find the eigenvectors via the solutions to the system of highly transcendental equations of Bethe-ansatz type which is presented in explicit form.The eigenvectors of the Hamiltonian ${\cal H}_{N}$ of $N$-sites quantum spin chains with elliptic exchange are connected with the double Bloch meromorphic solutions of the quantum continuous elliptic Calogero-Moser problem. This fact allows one to find the eigenvectors via the solutions to the system of highly transcendental equations of Bethe-ansatz type which is presented in explicit form.

arXiv:math-ph/9911022Nov 17, 19992 citations

Solution to three-magnon problem for S=1/2 periodic quantum spin chains with elliptic exchange

V. I. Inozemtsev

Journal of Mathematical PhysicsJan 1, 19968 citations

The Extended Bethe Ansatz for Infinite S = 1/2 Quantum Spin Chains with Non-Nearest-Neighbor Interaction

V. I. lnozemtsev

It is shown that the description of the states of infinite S = 1/2 interacting spin systems with the Hamiltonian H s J Z a2 sinh-Za(J / ) (~ 1) 2 j# t , j , l~Z 2 can be performed by studying the hyperbolic Calogero-Sutherland eigenvalue problem. The construction of multimagnon wave functions in each N-magnon sector is based on solutions of the set of linear algebraic equations which determine also the structure of zonal spherical functions on symmetric spaces X ~ = SL(N, H)/Sp(N) of negative curvature. The usual Bethe Ansatz for the XXX Heisenberg model corresponds to asymptotic forms of these wave functions at small values of a 1 or large distances between spins turned over the ferromagnetic ground state.It is shown that the description of the states of infinite S = 1/2 interacting spin systems with the Hamiltonian H s J Z a2 sinh-Za(J / ) (~ 1) 2 j# t , j , l~Z 2 can be performed by studying the hyperbolic Calogero-Sutherland eigenvalue problem. The construction of multimagnon wave functions in each N-magnon sector is based on solutions of the set of linear algebraic equations which determine also the structure of zonal spherical functions on symmetric spaces X ~ = SL(N, H)/Sp(N) of negative curvature. The usual Bethe Ansatz for the XXX Heisenberg model corresponds to asymptotic forms of these wave functions at small values of a 1 or large distances between spins turned over the ferromagnetic ground state.

Jan 1, 20050 citations

Exact solution of an S =1/2 Heisenberg antiferromagnetic chain with long-ranged interactions

B. Sriram Shastry

The S=1/2 Heisenberg Hamiltonian H=1/2${\mathcal{J}}_{\mathrm{n}=1}^{\mathrm{N}\mathrm{\ensuremath{-}}1}$ ${\mathcal{J}}_{\mathit{m}=1}^{\mathit{N}}$ ${\mathit{J}}_{\mathit{n}}$ ${\mathrm{\ensuremath{\sigma}}}_{\mathit{m}}$\ensuremath{\cdot} ${\mathrm{\ensuremath{\sigma}}}_{\mathit{m}+\mathit{n}}$, with ${J}_{n}$ = ${J}_{0}$ / ${\mathrm{sin}}^{2}$ (n\ensuremath{\pi}/N), is shown to have a simple singlet ground state in the form of a Jastrow function. The spectrum and correlations are explicitly known and the magnetic susceptibility is shown to be Pauli type at T=0. The model has a striking similarity to the nearest-neighbor isotropic Heisenberg model and may be viewed as a discretized version of the Sutherland-Calogero-Moser system.The S=1/2 Heisenberg Hamiltonian H=1/2${\mathcal{J}}_{\mathrm{n}=1}^{\mathrm{N}\mathrm{\ensuremath{-}}1}$${\mathcal{J}}_{\mathit{m}=1}^{\mathit{N}}$${\mathit{J}}_{\mathit{n}}$${\mathrm{\ensuremath{\sigma}}}_{\mathit{m}}$\ensuremath{\cdot} ${\mathrm{\ensuremath{\sigma}}}_{\mathit{m}+\mathit{n}}$, with ${J}_{n}$=${J}_{0}$/${\mathrm{sin}}^{2}$(n\ensuremath{\pi}/N), is shown to have a simple singlet ground state in the form of a Jastrow function. The spectrum and correlations are explicitly known and the magnetic susceptibility is shown to be Pauli type at T=0. The model has a striking similarity to the nearest-neighbor isotropic Heisenberg model and may be viewed as a discretized version of the Sutherland-Calogero-Moser system.

Physical Review LettersFeb 15, 1988769 citations

Integrable Heisenberg-van Vleck chains with variable range exchange

V. I. Inozemtsev

The review of recent results in the s=1/2 quantum spin chains with $1/\sinh^2(κr$ exchange is presented. Related problems in the theory of classical and quantum Calogero-Sutherland-Moser systems with inverse square hyperbolic and elliptic potentials are discussed. The attention is paid to finding the explicit form of corresponding Bethe-Ansatz equations and to connection with generalized Hubbard chains in one dimension.The review of recent results in the s=1/2 quantum spin chains with $1/\sinh^2(κr$ exchange is presented. Related problems in the theory of classical and quantum Calogero-Sutherland-Moser systems with inverse square hyperbolic and elliptic potentials are discussed. The attention is paid to finding the explicit form of corresponding Bethe-Ansatz equations and to connection with generalized Hubbard chains in one dimension.

arXiv:hep-th/0201001Jan 1, 200232 citations

Bethe Ansatz for Heisenberg XXX Model

Shao-shiung Lin, Shi-shyr Roan

We investigate Bethe Ansatz equations for the one-dimensional spin- $\frac{1}{2}$ Heisenberg XXX chain with a special interest in a finite system. Solutions for the two-particle sector are obtained. The ground state in antiferromagnetic case has been analytically studied through the logarithmic form of Bethe Ansatz equations.We investigate Bethe Ansatz equations for the one-dimensional spin-$\frac{1}{2}$ Heisenberg XXX chain with a special interest in a finite system. Solutions for the two-particle sector are obtained. The ground state in antiferromagnetic case has been analytically studied through the logarithmic form of Bethe Ansatz equations.

arXiv:cond-mat/9509183Oct 2, 19951 citation

The eigenvectors of the Hamiltonian

{\cal H}_{N}

N

-sites quantum spin chains with elliptic exchange are connected with the double Bloch meromorphic solutions of the quantum continuous elliptic Calogero-Moser problem. This fact allows one to find the eigenvectors via the solutions to the system of highly transcendental equations of Bethe-ansatz type which is presented in explicit form.

The S=1/2 Heisenberg Hamiltonian H=1/2${\mathcal{J}}_{\mathrm{n}=1}^{\mathrm{N}\mathrm{\ensuremath{-}}1}$

{\mathcal{J}}_{\mathit{m}=1}^{\mathit{N}}

{\mathit{J}}_{\mathit{n}}

${\mathrm{\ensuremath{\sigma}}}_{\mathit{m}}$\ensuremath{\cdot} ${\mathrm{\ensuremath{\sigma}}}_{\mathit{m}+\mathit{n}}$, with

{J}_{n}

{J}_{0}

{\mathrm{sin}}^{2}

(n\ensuremath{\pi}/N), is shown to have a simple singlet ground state in the form of a Jastrow function. The spectrum and correlations are explicitly known and the magnetic susceptibility is shown to be Pauli type at T=0. The model has a striking similarity to the nearest-neighbor isotropic Heisenberg model and may be viewed as a discretized version of the Sutherland-Calogero-Moser system.

The review of recent results in the s=1/2 quantum spin chains with

1/\sinh^2(κr

exchange is presented. Related problems in the theory of classical and quantum Calogero-Sutherland-Moser systems with inverse square hyperbolic and elliptic potentials are discussed. The attention is paid to finding the explicit form of corresponding Bethe-Ansatz equations and to connection with generalized Hubbard chains in one dimension.

We investigate Bethe Ansatz equations for the one-dimensional spin-

\frac{1}{2}

Heisenberg XXX chain with a special interest in a finite system. Solutions for the two-particle sector are obtained. The ground state in antiferromagnetic case has been analytically studied through the logarithmic form of Bethe Ansatz equations.