English
Related papers

Related papers: Fast analytic solver of rational Bethe equations

200 papers

The problem of constructing the $SL(N,\mathbb{C})$ invariant solutions to the Yang-Baxter equation is considered. The solutions ($\mathcal{R}$-operators) for arbitrarily principal series representations of $SL(N,\mathbb{C})$ are obtained in…

Exactly Solvable and Integrable Systems · Physics 2008-12-19 Sergey E. Derkachov , Alexander N. Manashov

We connect two alternative concepts of solving integrable models, Baxter's method of auxiliary matrices (or Q-operators) and the algebraic Bethe ansatz. The main steps of the calculation are performed in a general setting and a formula for…

Mathematical Physics · Physics 2009-11-10 Christian Korff

Generic inhomogeneous integrable XXZ chains with arbitrary spins are studied by means of the quantum separation of variables (SOV) method. Within this framework, a complete description of the spectrum (eigenvalues and eigenstates) of the…

Mathematical Physics · Physics 2014-11-25 G. Niccoli , V. Terras

We propose a Q-system for the $A_m^{(1)}$ quantum integrable spin chain. We also find compact determinant expressions for all the Q-functions, both for the rational and trigonometric cases.

High Energy Physics - Theory · Physics 2020-08-11 Rafael I. Nepomechie

We develop an approach for constructing the Baxter Q-operators for generic sl(N) spin chains. The key element of our approach is the possibility to represent a solution of the the Yang Baxter equation in the factorized form. We prove that…

Exactly Solvable and Integrable Systems · Physics 2009-02-12 S. E. Derkachov , A. N. Manashov

We construct a Q-operator for the open XXZ Heisenberg quantum spin chain with diagonal boundary conditions and give a rigorous derivation of Baxter's TQ relation. Key roles in the theory are played by a particular infinite-dimensional…

Mathematical Physics · Physics 2020-10-13 Bart Vlaar , Robert Weston

We prove an inversion identity for the open AdS/CFT SU(1|1) quantum spin chain which is exact for finite size. We use this identity, together with an analytic ansatz, to determine the eigenvalues of the transfer matrix and the corresponding…

High Energy Physics - Theory · Physics 2009-02-05 Rafael I. Nepomechie , Eric Ragoucy

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

We consider the Bethe equations for the isotropic spin-1/2 Heisenberg quantum spin chain with periodic boundary conditions. We formulate a conjecture for the number of solutions with pairwise distinct roots of these equations, in terms of…

Mathematical Physics · Physics 2013-11-20 Wenrui Hao , Rafael I. Nepomechie , Andrew J. Sommese

In this paper, we study and implement the structural iterative eigensolvers for the large-scale eigenvalue problem in the Bethe-Salpeter equation (BSE) based on the reduced basis approach via low-rank factorizations in generating matrices,…

Numerical Analysis · Mathematics 2017-03-08 Peter Benner , Sergey Dolgov , Venera Khoromskaia , Boris N. Khoromskij

Studying the Bethe-Salpeter formalism for interactions instantaneous in the rest frame of the bound states described, we show that, for bound-state constituents of arbitrary masses, the mass of the ground state of a given spin may be…

High Energy Physics - Phenomenology · Physics 2009-11-07 Wolfgang Lucha , F. F. Schoberl

We propose an extension of the numerical approach for integrable Richardson-Gaudin models based on a new set of eigenvalue-based variables. Starting solely from the Gaudin algebra, the approach is generalized towards the full class of XXZ…

Statistical Mechanics · Physics 2015-04-08 Pieter W. Claeys , Stijn De Baerdemacker , Mario Van Raemdonck , Dimitri Van Neck

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

We study open spin chains based on rational sl(N) and sl(M|N) R-matrices. We classify the solutions of the reflection equations, for both the soliton-preserving and soliton-non-preserving cases. We then write the Bethe equations for these…

Mathematical Physics · Physics 2007-05-23 D. Arnaudon , J. Avan , N. Crampe' , A. Doikou , L. Frappat , E. Ragoucy

We use the structural similarity of certain Coxeter Artin Systems to the Yang--Baxter and Reflection Equations to convert representations of these systems into new solutions of the Reflection Equation. We construct certain Bethe ansatz…

High Energy Physics - Theory · Physics 2008-11-26 A Doikou , P P Martin

We present an ``algebraic treatment'' of the analytical Bethe ansatz for open spin chains with soliton non preserving (SNP) boundary conditions. For this purpose, we introduce abstract monodromy and transfer matrices which provide an…

Mathematical Physics · Physics 2009-11-11 D. Arnaudon , N. Crampe , A. Doikou , L. Frappat , E. Ragoucy

We construct new integrable systems describing particles with internal spin from four-dimensional $\mathcal{N}=2$ quiver gauge theories. The models can be quantized and solved exactly using the quantum inverse scattering method and also…

High Energy Physics - Theory · Physics 2017-02-27 Nick Dorey , Peng Zhao

We develop Yang-Baxter integrability structures connected with the quantum affine superalgebra Uq(\hat sl(2|1)). Baxter's Q-operators are explicitly constructed as supertraces of certain monodromy matrices associated with (q-deformed)…

High Energy Physics - Theory · Physics 2009-01-23 Vladimir V. Bazhanov , Zengo Tsuboi

Bethe equations, whose solutions determine exact eigenvalues and eigenstates of corresponding integrable Hamiltonians, are generally hard to solve. We implement a Variational Quantum Eigensolver (VQE) approach to estimating Bethe roots of…

Quantum Physics · Physics 2025-01-28 David Raveh , Rafael I. Nepomechie

The Bethe ansatz, both in its coordinate and its algebraic version, is an exceptional method to compute the eigenvectors and eigenvalues of integrable systems. However, computing correlation functions using the eigenvectors thus constructed…

High Energy Physics - Theory · Physics 2023-12-25 Rafael Hernandez , Juan Miguel Nieto