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Related papers: Bethe's Quantum Numbers And Rigged Configurations

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Several quantum many-body models in one dimension possess exact solutions via the Bethe ansatz method, which has been highly successful for understanding their behavior. Nevertheless, there remain physical properties of such models for…

The Bethe Ansatz is a method for constructing exact eigenstates of quantum-integrable spin chains. Recently, deterministic quantum algorithms, referred to as "algebraic Bethe circuits", have been developed to prepare Bethe states for the…

Quantum Physics · Physics 2025-07-29 Roberto Ruiz , Alejandro Sopena , Esperanza López , Germán Sierra , Balázs Pozsgay

We prove the modified algebraic Bethe Ansatz characterization of the spectral problem for the closed XXX Heisenberg spin chain with an arbitrary twist and arbitrary positive (half)-integer spin at each site of the chain. We provide two…

Mathematical Physics · Physics 2019-09-09 Samuel Belliard , Nikita A. Slavnov , Benoit Vallet

Every solution of the Bethe ansatz equations (BAE) is characterized by a set of quantum numbers called the Bethe quantum numbers, which are fundamental for evaluating it numerically. We rigorously derive the Bethe quantum numbers for the…

Mathematical Physics · Physics 2024-09-10 Takashi Imoto , Tetsuo Deguchi

I derived Bethe Ansatz equations for two model Periodic Quantum Circuits: 1) XXZ model; 2) Chiral Hubbard Model. I obtained explicit expressions for the spectra of the strings of any length. These analytic results may be useful for…

Mesoscale and Nanoscale Physics · Physics 2021-07-14 I. L. Aleiner

The Bethe Ansatz is a method that is used in quantum integrable models in order to solve them explicitly. This method is explained here in a general framework, which applies to 1D quantum spin chains, 2D statistical lattice models (vertex…

solv-int · Physics 2007-05-23 P. Zinn-Justin

The spin-1/2 XYZ model with both periodic and anti-periodic boundary conditions is studied via the off-diagonal Bethe ansatz method. The exact spectra of the Hamiltonians and the Bethe ansatz equations are derived by constructing the…

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

We review the algebraic Bethe ansatz for the Heisenberg model. The exposition includes some of recent advancements with emphasis on a relation with the rigged configurations. We also provide somewhat thorough review of the crystal bases and…

Quantum Algebra · Mathematics 2017-04-07 Reiho Sakamoto

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…

Condensed Matter · Physics 2007-05-23 Shao-shiung Lin , Shi-shyr Roan

We compute the finite size spectrum for the spin 1/2 XXZ chain with twisted boundary conditions, for anisotropy in the regime $0< \gamma <\pi/2$, and arbitrary twist $\theta$. The string hypothesis is employed for treating complex…

High Energy Physics - Theory · Physics 2008-11-26 T. Nassar , O. Tirkkonen

We provide a basis transformation that inverts the coordinate Bethe Ansatz. It is widely believed that the Bethe Ansatz is complete, based on numerical evidence and combinatorial arguments. We present a constructive and comprehensive…

Mathematical Physics · Physics 2025-06-18 Eric I. Corwin , Nikolaus Elsaesser , Axel Saenz

The off-diagonal Bethe ansatz method is generalized to the high spin integrable systems associated with the su(2) algebra by employing the spin-s isotropic Heisenberg chain model with generic integrable boundaries as an example. With the…

Statistical Mechanics · Physics 2015-06-19 Junpeng Cao , Shuai Cui , Wen-Li Yang , Kangjie Shi , Yupeng Wang

In this note we construct Q-operators for the spin s open Heisenberg XXX chain with diagonal boundaries in the framework of the quantum inverse scattering method. Following the algebraic Bethe ansatz we diagonalise the introduced…

Mathematical Physics · Physics 2023-01-04 Rouven Frassek , István M. Szécsényi

The open spin-1/2 XXZ spin chain with diagonal boundary magnetic fields is the paradigmatic example of a quantum integrable model with open boundary conditions. We formulate a quantum algorithm for preparing Bethe states of this model,…

Quantum Physics · Physics 2022-01-26 John S. Van Dyke , Edwin Barnes , Sophia E. Economou , Rafael I. Nepomechie

We present a review of the method we have elaborated to compute the correlation functions of the XXZ spin-1/2 Heisenberg chain. This method is based on the resolution of the quantum inverse scattering problem in the algebraic Bethe Ansatz…

High Energy Physics - Theory · Physics 2007-05-23 N. Kitanine , J. M. Maillet , N. A. Slavnov , V. Terras

The off-diagonal Bethe Ansatz method [1] is used to revisit the periodic XXX Heisenberg spin-1/2 chain. It is found that the spectrum of the transfer matrix can be characterized by an inhomogeneous T-Q relation, a natural but nontrivial…

Mathematical Physics · Physics 2015-06-09 Yupeng Wang , Wen-Li Yang , Junpeng Cao , Kangjie Shi

Since a long-time, the quantum integrable systems have remained an area where modern mathematical methods have given an access to interesting results in the study of physical systems. The exact computations, both numerical and asymptotic,…

Mathematical Physics · Physics 2020-12-07 Giridhar V. Kulkarni

Bethe ansatz equations for spin-$s$ Heisenberg spin chain with $s\ge1$ are significantly more difficult to analyze than the spin-$\tfrac{1}{2}$ case, due to the presence of repeated roots. As a result, it is challenging to derive extra…

High Energy Physics - Theory · Physics 2024-05-01 Jue Hou , Yunfeng Jiang , Rui-Dong Zhu

A new exactly solvable one-dimensional spin-3/2 Heisenberg model with SO(5)-invariance is proposed. The eigenvalues and Bethe ansatz equations of the model are obtained by using the nested algebraic Bethe ansatz approach. Several exotic…

Strongly Correlated Electrons · Physics 2009-07-08 Yuzhu Jiang , Junpeng Cao , Yupeng Wang

We investigate the completeness of the solutions of the Bethe equations for the integrable spin-s isotropic (XXX) spin chain with periodic boundary conditions. Solutions containing the exact string i s, i (s-1), ..., -i(s-1), -is are…

Mathematical Physics · Physics 2015-06-18 Wenrui Hao , Rafael I. Nepomechie , Andrew J. Sommese