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

Physics Letters A

The Bethe ansatz, periodic boundary conditions and relations between various models

E. Berkcan, Leon N. Cooper, Udayan Mohanty

Published Jan 1, 1981• 0 citations
Publisher
DOI
10.1016/0375-9601(81)90054-2

Related papers

Spin- 12 XYZ model revisit: General solutions via off-diagonal Bethe ansatz

Junpeng Cao, Shuai Cui, Wen‐Li Yang +2 more

The spin-12 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 inhomogeneous T–Q relations, which allow us to treat both the even N (the number of lattice sites) and odd N cases simultaneously in a unified approach.

arXiv:1307.0280•Nuclear Physics B•Jul 3, 2014•60 citations

Exceptional solutions to the Bethe ansatz equations

L.V. Avdeev, Alexey A. Vladimirov

Theoretical and Mathematical Physics•Nov 1, 1986•50 citations

The algebraic Bethe Ansatz and combinatorial trees

R. S. Vieira, A. Lima-Santos

We study in this article the algebraic Bethe Ansatz from a combinatorial perspective.The commutation relations are represented by combinatorial diagrams so that the action of the transfer matrix over the nth excited state can be found through the analysis of some combinatorial trees.This allows us to compute the eigenvalues and eigenstates of the transfer matrix, as well as the respective Bethe Ansatz equations, in a straightforward way.As examples, we consider the six-vertex model with both periodic and non-periodic boundary conditions.In parallel, we also present a comprehensive introduction to the usual algebraic Bethe Ansatz (for both the periodic and the non-periodic cases).

arXiv:1707.02584•Journal of Integrable Systems•Jan 1, 2019•3 citations

A simple derivation of the higher-level Bethe ansatz equations

B -D Dorfel, Alexey A. Vladimirov

Physics Letters A•Apr 1, 1989•0 citations

Introduction to the Algebraic Bethe Ansatz

N. A. Slavnov

Trends in mathematics•Jan 1, 2020•1 citation

Off-diagonal Bethe Ansatz solution of the $τ_2$-model

Xiaotian Xu, Cao, Junpeng, Shuai Cui +3 more

The generic quantum $τ_2$-model (also known as Baxter-Bazhanov-Stroganov (BBS) model) with periodic boundary condition is studied via the off-diagonal Bethe Ansatz method. The eigenvalues of the corresponding transfer matrix (solutions of the recursive functional relations in $τ_j$-hierarchy) with generic site-dependent inhomogeneity parameters are given in terms of an inhomogeneous T-Q relation with polynomial Q-functions. The associated Bethe Ansatz equations are obtained. Numerical solutions of the Bethe Ansatz equations for small number of sites indicate that the inhomogeneous T-Q relation does indeed give the complete spectrum.

arXiv:1507.03367•Jul 13, 2015•0 citations
We study in this article the algebraic Bethe Ansatz from a combinatorial perspective.The commutation relations are represented by combinatorial diagrams so that the action of the transfer matrix over the nth excited state can be found through the analysis of some combinatorial trees.This allows us to compute the eigenvalues and eigenstates of the transfer matrix, as well as the respective Bethe Ansatz equations, in a straightforward way.As examples, we consider the six-vertex model with both periodic and non-periodic boundary conditions.In parallel, we also present a comprehensive introduction to the usual algebraic Bethe Ansatz (for both the periodic and the non-periodic cases).
Off-diagonal Bethe Ansatz solution of the τ2τ_2τ2​-model
The generic quantum τ2τ_2τ2​-model (also known as Baxter-Bazhanov-Stroganov (BBS) model) with periodic boundary condition is studied via the off-diagonal Bethe Ansatz method. The eigenvalues of the corresponding transfer matrix (solutions of the recursive functional relations in τjτ_jτj​-hierarchy) with generic site-dependent inhomogeneity parameters are given in terms of an inhomogeneous T-Q relation with polynomial Q-functions. The associated Bethe Ansatz equations are obtained. Numerical solutions of the Bethe Ansatz equations for small number of sites indicate that the inhomogeneous T-Q relation does indeed give the complete spectrum.