English
Related papers

Related papers: Exact solution of an su(n) spin torus

200 papers

We propose a Bethe-Ansatz-type solution of the open spin-1/2 integrable XXZ quantum spin chain with general integrable boundary terms and bulk anisotropy values i \pi/(p+1), where p is a positive integer. All six boundary parameters are…

High Energy Physics - Theory · Physics 2011-02-16 Rajan Murgan , Rafael I. Nepomechie , Chi Shi

In this contribution we review the theory of integrability of quantum systems in one spatial dimension. We introduce the basic concepts such as the Yang-Baxter equation, commuting currents, and the algebraic Bethe ansatz. Quite extensively…

Strongly Correlated Electrons · Physics 2009-11-11 Andreas Klümper

We consider integrable Matrix Product States (MPS) in integrable spin chains and show that they correspond to "operator valued" solutions of the so-called twisted Boundary Yang-Baxter (or reflection) equation. We argue that the…

Statistical Mechanics · Physics 2019-05-29 Balázs Pozsgay , Lorenzo Piroli , Eric Vernier

The $Q$-system is an efficient method for finding complete physical solutions of Bethe ansatz equations, but so far its application has been confined to systems possessing $U(1)$ symmetry. We extend the rational $Q$-system framework to…

High Energy Physics - Theory · Physics 2025-12-02 Yunfeng Jiang , Yi-Chao Liu , Yuan Miao , Zi-Xi Tan

The free energy per lattice site of a quantum spin chain in the thermodynamic limit is determined by a single `dominant' Eigenvalue of an associated quantum transfer matrix in the infinite Trotter number limit. For integrable quantum spin…

Mathematical Physics · Physics 2025-12-16 Saskia Faulmann , Frank Göhmann , Karol K. Kozlowski

We generalise the fusion procedure for the $A_{\n-1}^{(1)}$ open spin chain ($\n>2$) and we show that the transfer matrix satisfies a crossing property. We use these results to solve the $A_{\n-1}^{(1)}$ open spin chain with $U_{q}…

High Energy Physics - Theory · Physics 2008-11-26 Anastasia Doikou

We investigate the integrable structures in an N=2 superconfomal Sp(N) Yang-Mills theory with matter, which is dual to an open+closed string system. We restrict ourselves to the BMN operators that correspond to free string states. In the…

High Energy Physics - Theory · Physics 2009-11-10 Bin Chen , Xiao-Jun Wang , Yong-Shi Wu

We consider the open spin-s XXZ quantum spin chain with nondiagonal boundary terms. By exploiting certain functional relations at roots of unity, we derive a generalized form of T-Q relation involving more than one independent Q(u), which…

Mathematical Physics · Physics 2015-06-05 Rashad Baiyasi , Rajan Murgan

Using considerations based on the thermodynamical Bethe ansatz as well representation theory of twisted Yangians we derive an exact expression for the overlaps between the Bethe eigenstates of the $SO(6)$ spin chain and matrix product…

High Energy Physics - Theory · Physics 2022-07-19 Marius de Leeuw , Tamás Gombor , Charlotte Kristjansen , Georgios Linardopoulos , Balázs Pozsgay

We generalize our recent explicit construction of the full hierarchy of Baxter Q-operators of compact spin chains with su(n) symmetry to the supersymmetric case su(n|m). The method is based on novel degenerate solutions of the graded…

Mathematical Physics · Physics 2015-05-20 Rouven Frassek , Tomasz Lukowski , Carlo Meneghelli , Matthias Staudacher

The anisotropic spin-1/2 chains with arbitrary boundary fields are diagonalized with the off-diagonal Bethe ansatz method. Based on the properties of the R-matrix and the K-matrices, an operator product identity of the transfer matrix is…

Statistical Mechanics · Physics 2015-06-16 Junpeng Cao , Wen-Li Yang , Kangjie Shi , Yupeng Wang

The transfer matrix of the XXZ open spin-1/2 chain with general integrable boundary conditions and generic anisotropy parameter (q is not a root of unity and |q|=1) is diagonalized using the representation theory of the q-Onsager algebra.…

High Energy Physics - Theory · Physics 2015-06-26 P. Baseilhac , K. Koizumi

We solve the longstanding problem to define a functional characterization of the spectrum of the transfer matrix associated to the most general spin-1/2 representations of the 6-vertex reflection algebra for general inhomogeneous chains.…

Mathematical Physics · Physics 2017-03-17 N. Kitanine , J. -M. Maillet , G. Niccoli

Inspired by the integrable structures appearing in weakly coupled planar N=4 super Yang-Mills theory, we study Q-operators and Yangian invariants of rational integrable spin chains. We review the quantum inverse scattering method along with…

High Energy Physics - Theory · Physics 2014-12-11 Rouven Frassek

Exact solution of the quantum integrable $D^{(2)}_2$ spin chain with generic integrable boundary fields is constructed. It is found that the transfer matrix of this model can be factorized as the product of those of two open staggered…

Mathematical Physics · Physics 2022-04-28 Guang-Liang Li , Junpeng Cao , Wen-Li Yang , Kangjie Shi , Yupeng Wang

We diagonalize the double-row transfer matrix of the SU(N) vertex model for certain classes of non-diagonal boundary conditions. We derive explicit expressions for the corresponding eigenvectors and eigenvalues by means of the algebraic…

Exactly Solvable and Integrable Systems · Physics 2009-11-10 W. Galleas , M. J. Martins

We calculate the scalar product of Bethe states of the XXZ spin-$\frac{1}{2}$ chain with general integrable boundary conditions. The off-shell equations satisfied by the transfer matrix and the off-shell Bethe vectors allow one to derive a…

Mathematical Physics · Physics 2021-09-01 Samuel Belliard , Rodrigo A. Pimenta , Nikita A. Slavnov

We consider both closed and open integrable antiferromagnetic chains constructed with the SU(N)-invariant R matrix. For the closed chain, we extend the analyses of Sutherland and Kulish-Reshetikhin by considering also complex ``string''…

High Energy Physics - Theory · Physics 2009-10-31 Anastasia Doikou , Rafael I. Nepomechie

In [1] an integrable quantum model was introduced and a class of its cyclic representations was proven to define lattice regularizations of the Sine-Gordon model. Here, we analyze general cyclic representations of this integrable quantum…

Mathematical Physics · Physics 2011-03-31 G. Niccoli

An $U_q(sl(n))$ invariant transfer matrix with periodic boundary conditions is analysed by means of the algebraic nested Bethe ansatz for the case of $q$ being a root of unity. The transfer matrix corresponds to a 2-dimensional vertex model…

High Energy Physics - Theory · Physics 2009-10-22 M. Karowski , A. Zapletal