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Related papers: On Generalized $Q$-systems

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The XXX Gaudin model with generic integrable boundaries specified by the most general non-diagonal K-matrices is studied by the off-diagonal Bethe ansatz method. The eigenvalues of the associated Gaudin operators and the corresponding Bethe…

Mathematical Physics · Physics 2015-03-10 Kun Hao , Junpeng Cao , Tao Yang , Wen-Li Yang

We propose a generalization of the algebraic Bethe ansatz to obtain the eigenvectors of the Heisenberg spin chain with general boundaries associated to the eigenvalues and the Bethe equations found recently by Cao et al. The ansatz takes…

Mathematical Physics · Physics 2013-11-25 Samuel Belliard , Nicolas Crampé

Several studies have exploited the integrable structure of central spin models to deepen understanding of these fundamental systems. In recent years, an underlying supersymmetry for systems with XX interactions has been uncovered. Here we…

Exactly Solvable and Integrable Systems · Physics 2023-04-03 W J P van Tonder , J Links

The quantum integrable systems associated with the quantum loop algebras $\mathrm U_q(\mathcal L(\mathfrak{sl}_{\, l + 1}))$ are considered. The factorized form of the transfer operators related to the infinite dimensional evaluation…

Mathematical Physics · Physics 2021-08-25 A. V. Razumov

We consider an open spin chain model with GL(N) bulk symmetry that is broken to GL(M) x GL(N-M) by the boundary, which is a generalization of a model arising in string/gauge theory. We prove the integrability of this model by constructing…

High Energy Physics - Theory · Physics 2015-05-14 Rafael I. Nepomechie

We consider the critical alternating quantum spin chain with ${q_{+}\over 2}$, ${q_{-} \over2}$ spins. Using the Bethe ansatz technique we find explicit expressions for the $S$-matrix of the model. We show that in the limit that $q_{\pm}…

High Energy Physics - Theory · Physics 2009-11-07 Anastasia Doikou , Andrei Babichenko

We consider the open spin-s XXZ quantum spin chain with nondiagonal boundary terms. By exploiting certain functional relations at roots of unity, we propose the Bethe ansatz solution for the transfer matrix eigenvalues for cases where…

High Energy Physics - Theory · Physics 2009-11-19 Rajan Murgan

The Algebraic Bethe Ansatz (ABA) is a highly successful analytical method used to exactly solve several physical models in both statistical mechanics and condensed-matter physics. Here we bring the ABA into unitary form, for its direct…

We study the P"oschl-Teller equation in complex domain and deduce infinite families of TQ and Bethe ansatz equations, classified by four integers. In all these models the form of T is very simple, while Q can be explicitly written in terms…

High Energy Physics - Theory · Physics 2008-11-26 Patrick Dorey , Junji Suzuki , Roberto Tateo

This monograph introduces the reader to basic notions of integrable techniques for one-dimensional quantum systems. In a pedagogical way, a few examples of exactly solvable models are worked out to go from the coordinate approach to the…

Statistical Mechanics · Physics 2017-06-23 Fabio Franchini

The thermodynamic Bethe ansatz approach to the study of integrable quantum field theories was introduced in the early 90s. Since then it has been known that the thermodynamic Bethe ansatz equations can be recast in the form of $Y$-systems.…

High Energy Physics - Theory · Physics 2022-10-03 Olalla A. Castro-Alvaredo

We discuss a simple procedure for obtaining new integrable spin chains from old by replacing each single state of the original model by some collection of states. This works whenever the Lax matrix of the chain has a certain form. The…

Mathematical Physics · Physics 2010-05-19 David Kagan , Charles A. S. Young

Models generalizing the su(2) XX spin-chain were recently introduced. These XXC models also have an underlying su(2) structure. Their construction method is shown to generalize to the chains based on the fundamental representations of the…

solv-int · Physics 2007-05-23 Z. Maassarani

In this paper we propose a simple method for building exactly solvable multi-parameter spectral equations which in turn can be used for constructing completely integrable and exactly solvable quantum systems. The method is based on the use…

High Energy Physics - Theory · Physics 2007-05-23 Dieter Mayer , Alexander Ushveridze , Zbigniew Walczak

We review recent progress towards the solution of exactly solved isotropic vertex models with arbitrary toroidal boundary conditions. Quantum space transformations make it possible the diagonalization of the corresponding transfer matrices…

Exactly Solvable and Integrable Systems · Physics 2007-05-23 M. J. Martins

We formulate the inverse scattering method for a periodic box-ball system and solve the initial value problem. It is done by a synthesis of the combinatorial Bethe ansa"tze at q=1 and q=0, which provides the ultradiscrete analogue of…

Quantum Algebra · Mathematics 2009-11-11 Atsuo Kuniba , Taichiro Takagi , Akira Takenouchi

We discuss the relation between the cluster integrable systems and $q$-difference Painlev\'e equations. The Newton polygons corresponding to these integrable systems are all 16 convex polygons with a single interior point. The Painlev\'e…

Mathematical Physics · Physics 2018-02-19 M. Bershtein , P. Gavrylenko , A. Marshakov

A general method is proposed for constructing the Bethe ansatz equations of integrable models without U(1) symmetry. As an example, the exact spectrum of the XXZ spin ring with M{\" o}bius like topological boundary condition is derived by…

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

We study the spectrum of the integrable open XXX Heisenberg spin chain subject to non-diagonal boundary magnetic fields. The spectral problem for this model can be formulated in terms of functional equations obtained by separation of…

Statistical Mechanics · Physics 2011-03-07 Holger Frahm , Jan H. Grelik , Alexander Seel , Tobias Wirth

We consider the preparation of all the eigenstates of spin chains using quantum circuits. It is known that generic eigenstates of free-fermionic spin chains can be prepared with circuits whose depth grows only polynomially with the length…

Quantum Physics · Physics 2025-09-16 Roberto Ruiz , Alejandro Sopena , Balázs Pozsgay , Esperanza López