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A model describing coherent quantum tunneling between two trapped Bose-Einstein condensates is shown to admit an exact solution. The spectrum is obtained by the algebraic Bethe ansatz. An asymptotic analysis of the Bethe ansatz equations…

Mesoscale and Nanoscale Physics · Physics 2009-11-07 Huan-Qiang Zhou , Jon Links , Ross H. McKenzie , Xi-Wen Guan

We examine the question of whether Bethe's ansatz reproduces all states in the periodic Heisenberg XXZ and XXX spin chains. As was known to Bethe himself, there are states for which the Bethe momenta $k_n$ diverge: these are in fact the…

Strongly Correlated Electrons · Physics 2007-05-23 Rahul Siddharthan

Two integrable quantum spin ladder systems will be introduced associated with the fundamental su(2|2) solution of the Yang-Baxter equation. The first model is a generalized quantum Ising system with Ising rung interactions. In the second…

Strongly Correlated Electrons · Physics 2007-05-23 A. Foerster , K. E. Hibberd , J. R. Links , I. Roditi

Vertex models with quantum group symmetry give rise to integrable cellular automata at q=0. We study a prototype example known as the periodic box-ball system. The initial value problem is solved in terms of an ultradiscrete analogue of the…

Quantum Algebra · Mathematics 2009-11-11 Atsuo Kuniba , Reiho Sakamoto

We study the diagonalization problem of certain Hofstadter-type models through the algebraic Bethe ansatz equation by the algebraic geometry method. When the spectral variables lie on a rational curve, we obtain the complete and explicit…

Condensed Matter · Physics 2008-11-26 Shao-shiung Lin , Shi-shyr Roan

We evaluate the superconformal index using the Bethe Ansatz (BA) approach for 4d $\mathcal{N}=1$ toric quiver gauge theories with a small amount of gauge groups. We restrict to $\mathrm{SU}(2)$ gauge factors and compare the results with the…

High Energy Physics - Theory · Physics 2025-06-19 Antonio Amariti , Pietro Glorioso

We consider the problem of analytically continuing energies computed with the Bethe ansatz, as posed by the study of non-compact integrable spin chains. By introducing an imaginary extensive twist in the Bethe equations, we show that one…

Mathematical Physics · Physics 2020-08-25 Etienne Granet , Jesper Lykke Jacobsen , Hubert Saleur

With the off-diagonal Bethe ansatz method proposed recently by the present authors, we exactly diagonalize the $XXX$ spin chain with arbitrary boundary fields. By constructing a functional relation between the eigenvalues of the transfer…

Mathematical Physics · Physics 2015-06-16 Junpeng Cao , Wenli Yang , Kangjie Shi , Yupeng Wang

We show that the stochastic dynamics of a large class of one-dimensional interacting particle systems may be presented by integrable quantum spin Hamiltonians. Using the Bethe ansatz and similarity transformations this yields new exact…

Condensed Matter · Physics 2007-05-23 Gunter M. Schütz

In this paper, the algebraic Bethe ansatz with periodic boundary conditions is used to investigate trigonometric vertex models associated with the fundamental representations of the non-exceptional Lie algebras. This formulation allow us to…

Exactly Solvable and Integrable Systems · Physics 2011-02-16 A. Lima-Santos

A random tiling of rectangles and triangles displaying a decagonal phase is solved by Bethe Ansatz. Analogously to the solutions of the dodecagonal square triangle and the octagonal rectangle triangle tiling an exact expression for the…

Statistical Mechanics · Physics 2009-10-30 Jan de Gier , Bernard Nienhuis

We study two extended Bose-Hubbard-type Hamiltonians representing bosonic networks restricted to the graph of a cube. For both Hamiltonians, we demonstrate that Bethe ansatz methods of solution can be employed after applying a canonical…

Mathematical Physics · Physics 2026-02-06 Lachlan Bennett , Phillip S. Isaac , Jon Links

Recent interest in discrete, classical integrable systems has focused on their connection to quantum integrable systems via the Bethe equations. In this note, solutions to the rational nested Bethe ansatz (RNBA) equations are constructed…

Mathematical Physics · Physics 2007-05-23 Alex Kasman

We establish a correspondence between classical $A_n^{(1)}$ affine Toda field theories and $A_n$ Bethe Ansatz systems. We show that the connection coefficients relating specific solutions of the associated classical linear problem satisfy…

Mathematical Physics · Physics 2015-06-18 Panagiota Adamopoulou , Clare Dunning

The rational $Q$-system is an efficient method to solve Bethe ansatz equations for quantum integrable spin chains. We construct the rational $Q$-systems for generic Bethe ansatz equations described by an $A_{\ell-1}$ quiver, which include…

High Energy Physics - Theory · Physics 2023-03-15 Jie Gu , Yunfeng Jiang , Marcus Sperling

The construction of analytic solutions for quasi-exactly solvable systems is an interesting problem. We revisit a class of models for which the odd solutions were largely missed previously in the literature: the anharmonic oscillator, the…

Mathematical Physics · Physics 2024-09-17 Siyu Li , Ian Marquette , Yao-Zhong Zhang

This paper shows that sequential statistical analysis techniques can be generalised to the problem of selecting between alternative forecasting methods using scoring rules. A return to basic principles is necessary in order to show that…

Statistics Theory · Mathematics 2025-05-15 David T. Frazier , Donald S. Poskitt

We obtain recursion formulas for the Bethe vectors of models with periodic boundary conditions solvable by the nested algebraic Bethe ansatz and based on the quantum affine algebra $U_q(\widehat{\mathfrak{gl}}_{n})$. We also present a sum…

Mathematical Physics · Physics 2018-03-01 A. Hutsalyuk , A. Liashyk , S. Z. Pakuliak , E. Ragoucy , N. A. Slavnov

In this note we report the results of our study of a 1D integrable spin chain whose critical behaviour is governed by a CFT possessing a continuous spectrum of scaling dimensions. It is argued that the computation of the density of Bethe…

High Energy Physics - Theory · Physics 2020-10-22 Vladimir V. Bazhanov , Gleb A. Kotousov , Sergii M. Koval , Sergei L. Lukyanov

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