Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:cond-mat/9602105 · Journal of Physics A Mathematical and General

Integrable spin chain with reflecting end

Takashi Yamamoto, Osamu Tsuchiya

Published Jul 21, 1996• 38 citations
arXivHTMLPDF

Abstract

A new integrable spin chain of the Haldane - Shastry type is introduced. It is interpreted as the inverse-square interacting spin chain with a reflecting end. The lattice sites of this model consist of the square roots of the zeros of the Laguerre polynomial. Using the `exchange operator formalism', the integrals of motion for the model are explicitly constructed.

DOI
10.1088/0305-4470/29/14/021

Related papers

Conservation laws of the Haldane-Shastry type spin chains

Cao, Junpeng, Peng cheng He, Yuzhu Jiang +1 more

A systematic method to construct the complete set of conserved quantities of the Haldane-Shastry type spin chains is proposed. The hidden relationship between the Yang-Baxter relation and the conservation laws of the long-range interacting integrable models is exposed explicitly. An integrable anisotropic Haldane-Shastry model is also constructed.

arXiv:0811.4476•Nov 27, 2008•0 citations

Lattice integrable systems of Haldane-Shastry type

Alexios P. Polychronakos

We present a new lattice integrable system in one dimension of the Haldane-Shastry type. It consists of spins positioned at the static equilibrium positions of particles in a corresponding classical Calogero system and interacting through an exchange term with strength inversely proportional to the square of their distance. We achieve this by viewing the Haldane-Shastry system as a high-interaction limit of the Sutherland system of particles with internal degrees of freedom and identifying the same limit in a corresponding Calogero system. The commuting integrals of motion of this system are found using the exchange operator formalism.

arXiv:hep-th/9210109•Physical Review Letters•Apr 12, 1993•193 citations

Exactly Solvable SU(M) Spin Chain with Long-Range Interactions*

Hirohito Kiwata, Yasuhiro Akutsu

We present an exactly solvable quantum SU( M ) ( M : arbitrary integer ≥2) spin chain with long-range ( ∼ inverse-square) interactions. The model generalizes the so-called Haldane-Shastry system which corresponds to M =2. We find the Lax pair for the system which guarantees the integrability of the system. An exact many-body ground-state wave function with particular symmetry is explicitly constructed.

Journal of the Physical Society of Japan•May 15, 1992•9 citations

NEW FAMILY OF SOLVABLE 1D HEISENBERG MODELS

Holger Frahm, Vladimir I. Inozemtsev

Starting from a Calogero--Sutherland model with hyperbolic interaction confined by an external field with Morse potential we construct a Heisenberg spin chain with exchange interaction $\propto 1/\sinh^2 x$ on a lattice given in terms of the zeroes of Laguerre polynomials. Varying the strength of the Morse potential the Haldane--Shastry and harmonic spin chains are reproduced. The spectrum of the models in this class is found to be that of a classical one-dimensional Ising chain with nonuniform nearest neighbour coupling in a nonuniform magnetic field which allows to study the thermodynamics in the limit of infinite chains.

•Jan 1, 1994•21 citations

Integrability and Applications of the Exactly-Solvable Haldane-Shastry One-Dimensional Quantum Spin Chain

J. C. Talstra

Recently, the one dimensional model of $N$ spins with $S=\frac{1}{2}$ on a circle, interacting with an exchange that falls off with the inverse square of the separation: $H_{\rm ISE} =\sum_{i\neq j} \frac{1}{[\frac{N}π \sin(\frac{i-j}{N}π)]^2}(\svec_i\cdot \svec_j-\frac{1}{4})$, or ISE-model, has received ample attention. Its special features include: relatively simple eigenfunctions, non-interacting elementary excitations that obey semionic statistics (spinons), and a large ``quantum group'' symmetry algebra called the Yangian. This model is fully integrable, albeit in a slightly different sense than the more traditional nearest neighbor exchange (NNE) Heisenberg chain. This thesis comes in 4 chapters. Chapter 1 introduces the model and presents the construction of a subset of the eigenfunctions. The other eigenfunctions are shown to be generated by the action of the Yangian symmetry algebra of $H_{\rm ISE}$. Chapter 2 presents a method to construct the set of constants of the motion of the ISE-model. The ISE-model is tractable enough to obtain its zero-magnetic-field dynamical structure factors. Chapter 3 attempts to extend this to a non-zero magnetic field, where, due to the presence of spinons in the groundstate, more complicated excitations contribute: small numbers of magnons and spinons. discuss the relation to the more complicated NNE-model. Finally chapter 4 illustrates how a recently conjectured new form of Off Diagonal Long Range Order in antiferromagnetic spin chains can be reinterpreted as a spinon propagator in the ISE-model, and verified numerically. We briefly comment on its relevance to stabilizing superconductivity in the layered cuprates.

arXiv:cond-mat/9509178•Sep 30, 1995•4 citations

New family of solvable 1D Heisenberg models

H Frahm, V I Inozemtsev

Starting from a Calogero-Sutherland model with the hyperbolic interaction confined by an external field with Morse potential, we construct a Heisenberg spin chain with exchange interaction varies as 1/sinh 2 x on a lattice given in terms of the zeros of Laguerre polynomials. Varying the strength of the Morse potential, the Haldane-Shastry and harmonic spin chains are reproduced. The spectrum of the models in this class is found to be that of a classical one-dimensional Ising chain with non-uniform nearest-neighbour coupling in a non-uniform magnetic field which allows us to study the thermodynamics in the limit of infinite chains.

arXiv:cond-mat/9405038•Journal of Physics A Mathematical and General•Nov 7, 1994•39 citations
A new integrable spin chain of the Haldane - Shastry type is introduced. It is interpreted as the inverse-square interacting spin chain with a reflecting end. The lattice sites of this model consist of the square roots of the zeros of the Laguerre polynomial. Using the `exchange operator formalism', the integrals of motion for the model are explicitly constructed.
We present a new lattice integrable system in one dimension of the Haldane-Shastry type. It consists of spins positioned at the static equilibrium positions of particles in a corresponding classical Calogero system and interacting through an exchange term with strength inversely proportional to the square of their distance. We achieve this by viewing the Haldane-Shastry system as a high-interaction limit of the Sutherland system of particles with internal degrees of freedom and identifying the same limit in a corresponding Calogero system. The commuting integrals of motion of this system are found using the exchange operator formalism.
Starting from a Calogero--Sutherland model with hyperbolic interaction confined by an external field with Morse potential we construct a Heisenberg spin chain with exchange interaction ∝1/sinh⁡2x\propto 1/\sinh^2 x∝1/sinh2x on a lattice given in terms of the zeroes of Laguerre polynomials. Varying the strength of the Morse potential the Haldane--Shastry and harmonic spin chains are reproduced. The spectrum of the models in this class is found to be that of a classical one-dimensional Ising chain with nonuniform nearest neighbour coupling in a nonuniform magnetic field which allows to study the thermodynamics in the limit of infinite chains.
Recently, the one dimensional model of NNN spins with S=12S=\frac{1}{2}S=21​ on a circle, interacting with an exchange that falls off with the inverse square of the separation: $H_{\rm ISE} =\sum_{i\neq j} \frac{1}{[\frac{N}π \sin(\frac{i-j}{N}π)]^2}(\svec_i\cdot \svec_j-\frac{1}{4})$, or ISE-model, has received ample attention. Its special features include: relatively simple eigenfunctions, non-interacting elementary excitations that obey semionic statistics (spinons), and a large ``quantum group'' symmetry algebra called the Yangian. This model is fully integrable, albeit in a slightly different sense than the more traditional nearest neighbor exchange (NNE) Heisenberg chain. This thesis comes in 4 chapters. Chapter 1 introduces the model and presents the construction of a subset of the eigenfunctions. The other eigenfunctions are shown to be generated by the action of the Yangian symmetry algebra of HISEH_{\rm ISE}HISE​. Chapter 2 presents a method to construct the set of constants of the motion of the ISE-model. The ISE-model is tractable enough to obtain its zero-magnetic-field dynamical structure factors. Chapter 3 attempts to extend this to a non-zero magnetic field, where, due to the presence of spinons in the groundstate, more complicated excitations contribute: small numbers of magnons and spinons. discuss the relation to the more complicated NNE-model. Finally chapter 4 illustrates how a recently conjectured new form of Off Diagonal Long Range Order in antiferromagnetic spin chains can be reinterpreted as a spinon propagator in the ISE-model, and verified numerically. We briefly comment on its relevance to stabilizing superconductivity in the layered cuprates.
Starting from a Calogero-Sutherland model with the hyperbolic interaction confined by an external field with Morse potential, we construct a Heisenberg spin chain with exchange interaction varies as 1/sinh 2 x on a lattice given in terms of the zeros of Laguerre polynomials. Varying the strength of the Morse potential, the Haldane-Shastry and harmonic spin chains are reproduced. The spectrum of the models in this class is found to be that of a classical one-dimensional Ising chain with non-uniform nearest-neighbour coupling in a non-uniform magnetic field which allows us to study the thermodynamics in the limit of infinite chains.