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Related papers: Landscapes of integrable long-range spin chains

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We show that the anisotropic Heisenberg-Ising chains with higher spin allow, for special values of the anisotropy, integrable deformations intimately related to the theory of quantum groups at roots of unity. For the spin one case we…

High Energy Physics - Theory · Physics 2009-10-22 C. Gomez , G. Sierra

We consider a general class of boundary terms of the open XYZ spin-1/2 chain compatible with integrability. We have obtained the general elliptic solution of $K$-matrix obeying the boundary Yang-Baxter equation using the $R$-matrix of the…

High Energy Physics - Theory · Physics 2009-10-28 Takeo Inami , Hitoshi Konno

We present a recursion relation for the explicit construction of integrable spin chain Hamiltonians with long-range interactions. Based on arbitrary short-range (e.g. nearest-neighbor) integrable spin chains, it allows to construct an…

High Energy Physics - Theory · Physics 2015-03-13 Till Bargheer , Niklas Beisert , Florian Loebbert

We revisit the so-called folded XXZ model, which was treated earlier by two independent research groups. We argue that this spin-1/2 chain is one of the simplest quantum integrable models, yet it has quite remarkable physical properties.…

Statistical Mechanics · Physics 2021-10-13 Balázs Pozsgay , Tamás Gombor , Arthur Hutsalyuk , Yunfeng Jiang , Levente Pristyák , Eric Vernier

We consider the spin-one Motzkin chain with area weight $t>0$. We resolve three questions from the literature about this model. We prove (i) existence of a uniform spectral gap for all $t<1$ as conjectured by Zhang--Ahmadein--Klich…

Quantum Physics · Physics 2026-05-26 Radu Andrei , Marius Lemm , Ramis Movassagh

We introduce a new class of open, translationally invariant spin chains with long-range interactions depending on both spin permutation and (polarized) spin reversal operators, which includes the Haldane-Shastry chain as a particular…

Statistical Mechanics · Physics 2020-09-07 B. Basu-Mallick , F. Finkel , A. González-López

We derive a multiple integral representing the ground state density matrix of a segment of length $m$ of the XXZ spin chain on $L$ lattice sites, which depends on $L$ only parametrically. This allows us to treat chains of arbitrary finite…

Statistical Mechanics · Physics 2011-09-02 Jens Damerau , Frank Göhmann , Nils P. Hasenclever , Andreas Klümper

By a combination of analytical and numerical techniques, we analyze the continuum limit of the integrable 3\otimes\bar{3}\otimes 3\otimes\bar{3}... sl(2/1) superspin chain. We discover profoundly new features, including a continuous…

Disordered Systems and Neural Networks · Physics 2010-04-05 Fabian H. L. Essler , Holger Frahm , Hubert Saleur

The procedure for obtaining integrable open spin chain Hamiltonians via reflection matrices is explicitly carried out for some three-state vertex models. We have considered the 19-vertex models of Zamolodchikov-Fateev and Izergin-Korepin,…

Exactly Solvable and Integrable Systems · Physics 2014-11-18 E. C. Fireman , A. Lima-Santos , W. Utiel

Integrable Hamiltonians for higher spin periodic XXZ chains are constructed in terms of the spin generators; explicit examples for spins up to 3/2 are given. Relations between Hamiltonians for some U_q(sl_2)-symmetric and U(1)-symmetric…

High Energy Physics - Theory · Physics 2009-11-07 Andrei G. Bytsko

The hierarchy of Integrable Spin Chain Hamiltonians, which are trigonometric analogs of the Haldane Shastry Model and of the associated higher conserved charges, is derived by a reduction from the trigonometric Dynamical Models of…

High Energy Physics - Theory · Physics 2008-02-03 Denis Uglov

We study descendants of inhomogeneous vertex models with boundary reflections when the spin-spin scattering is assumed to be quasi--classical. This corresponds to consider certain power expansion of the boundary-Yang-Baxter equation (or…

Statistical Mechanics · Physics 2007-05-23 Antonio Di Lorenzo , Luigi Amico , Kazuhiro Hikami , Andreas Osterloh , Gaetano Giaquinta

An explicit construction for Q-operators of the finite XXZ spin-chain with twisted boundary conditions is presented. The massless and the massive regime is considered as well as the root of unity case. It is explained how these results…

High Energy Physics - Theory · Physics 2014-11-18 Christian Korff

We present new integrable models of interacting spin-1/2 chains, which can be interpreted as hard rod deformations of the XXZ Heisenberg chains. The models support multiple particle types: dynamical hard rods of length $\ell$ and particles…

Statistical Mechanics · Physics 2022-01-05 Balázs Pozsgay , Tamás Gombor , Arthur Hutsalyuk

In this paper we study Inozemtsev's su(m) quantum spin model with hyperbolic interactions and the associated spin chain of Haldane-Shastry type introduced by Frahm and Inozemtsev. We compute the spectrum of Inozemtsev's model, and use this…

Mathematical Physics · Physics 2014-11-20 J. C. Barba , F. Finkel , A. Gonzalez-Lopez , M. A. Rodriguez

Several complete systems of integrability conditions on a spin chain Hamiltonian density matrix are presented. The corresponding formulas for $R$-matrices are also given. The latter is expressed via the local Hamiltonian density in the form…

Exactly Solvable and Integrable Systems · Physics 2007-05-23 P. N. Bibikov

We classify all fundamental integrable spin chains with two-dimensional local Hilbert space which have regular R-matrices of difference form. This means that the R-matrix underlying the integrable structures is of the form R(u,v)=R(u-v) and…

Mathematical Physics · Physics 2020-04-01 Marius de Leeuw , Anton Pribytok , Paul Ryan

In this contribution we briefly review recent developments in the theory of long-range integrable spin chains. These spin chains constitute a natural generalisation of the well-studied integrable nearest-neighbour chains and are of…

High Energy Physics - Theory · Physics 2015-05-20 Adam Rej

We present an integrability-preserving recursion relation for the explicit construction of long-range spin chain Hamiltonians. These chains are generalizations of the Haldane-Shastry and Inozemtsev models and they play an important role in…

High Energy Physics - Theory · Physics 2012-08-28 Till Bargheer , Niklas Beisert , Florian Loebbert

We consider the integrable one-dimensional spin-$1$ chain defined by the Zamolodchikov-Fateev (ZF) Hamiltonian. The latter is parametrized, analogously to the XXZ spin-$1/2$ model, by a continuous anisotropy parameter and at the isotropic…

Statistical Mechanics · Physics 2016-05-23 Lorenzo Piroli , Eric Vernier