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Related papers: On quantum separation of variables

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We generalize the nested off-diagonal Bethe ansatz method to study the quantum chain associated with the twisted $D^{(2)}_3$ algebra (or the $D^{(2)}_3$ model) with either periodic or integrable open boundary conditions. We obtain the…

Mathematical Physics · Physics 2022-03-28 Guang-Liang Li , Xiaotian Xu , Kun Hao , Pei Sun , Junpeng Cao , Wen-Li Yang , Kangjie Shi , Yupeng Wang

We consider a Sturm-Liouville operator on a finite interval as well as a scattering problem on the real line both with transfer conditions at the origin. On a finite interval we show that the the Titchmarsh-Weyl $m$-function can be uniquely…

Spectral Theory · Mathematics 2018-04-20 Sonja Currie , Marlena Nowaczyk , Bruce A. Watson

We propose a basis for rational gl(N) spin chains in an arbitrary rectangular representation $(S^A)$ that factorises the Bethe vectors into products of Slater determinants in Baxter Q-functions. This basis is constructed by repeated action…

Mathematical Physics · Physics 2020-03-11 Paul Ryan , Dmytro Volin

Non-invertible categorical symmetries have emerged as a powerful tool to uncover new beyond-Landau phases of matter, both gapped and gapless, along with second order phase transitions between them. The general theory of such phases in…

Strongly Correlated Electrons · Physics 2026-05-13 Lakshya Bhardwaj , Lea E. Bottini , Sakura Schafer-Nameki , Apoorv Tiwari

This work is based on the author's PhD thesis. The main result of the thesis is the use of the boost operator to develop a systematic method to construct new integrable spin chains with nearest-neighbour interaction and characterized by an…

Statistical Mechanics · Physics 2023-12-04 Chiara Paletta

In our previous paper math.QA/0412192 the Cayley-Hamilton identity for the GL(m|n) type quantum matrix algebra was obtained. Here we continue investigation of that identity. We derive it in three alternative forms and, most importantly, we…

Quantum Algebra · Mathematics 2007-05-23 Dimitri Gurevich , Pavel Pyatov , Pavel Saponov

The antiperiodic transfer matrix associated to higher spin representations of the rational 6-vertex Yang-Baxter algebra is analyzed by generalizing the approach introduced recently in [1], for the cyclic representations, in [2], for the…

Mathematical Physics · Physics 2013-06-04 G. Niccoli

The subject of this thesis is the rigorous construction of QFT models with nontrivial interaction. Two different approaches in the framework of AQFT are discussed. On the one hand, an inverse scattering problem is considered. A given…

Mathematical Physics · Physics 2015-03-04 Sabina Alazzawi

We explicitly construct an integrable and strongly interacting dissipative quantum circuit via a trotterization of the Hubbard model with imaginary interaction strength. To prove integrability, we build an inhomogeneous transfer matrix,…

Statistical Mechanics · Physics 2021-03-22 Lucas Sá , Pedro Ribeiro , Tomaž Prosen

This article, based on the author's PhD thesis, reviews recent advancements in the field of quantum integrability, in particular the separation of variables (SoV) program for high-rank integrable spin chains and the boost mechanism for…

Mathematical Physics · Physics 2022-01-31 Paul Ryan

We show how any integrable 2D QFT enjoys the existence of infinitely many non--abelian {\it conserved} charges satisfying a Yang--Baxter symmetry algebra. These charges are generated by quantum monodromy operators and provide a…

High Energy Physics - Theory · Physics 2011-07-19 C. Destri , H. J. de Vega

In this paper we construct separated variables for quantum integrable models related to the algebra $U_q(\hat{sl}_N)$. This generalizes the results by Sklyanin for $N=2,3$.

Mathematical Physics · Physics 2007-05-23 Feodor A. Smirnov

We introduce and study a class of two-dimensional integrable quantum field theories that carry an internal $\mathbb{Z}_n$ structure. These models extend factorised scattering beyond the conventional framework, featuring both the usual…

High Energy Physics - Theory · Physics 2025-11-25 Nicolò Brizio , Tommaso Morone , Nicolò Primi , Roberto Tateo

We pursue our study of the antiperiodic dynamical 6-vertex model using Sklyanin's separation of variables approach, allowing in the model new possible global shifts of the dynamical parameter. We show in particular that the spectrum and…

Mathematical Physics · Physics 2016-04-20 D. Levy-Bencheton , G. Niccoli , V. Terras

A new integrable model which is a variant of the one-dimensional Hubbard model is proposed. The integrability of the model is verified by presenting the associated quantum R-matrix which satisfies the Yang-Baxter equation. We argue that the…

Strongly Correlated Electrons · Physics 2015-06-24 X. -W. Guan , A. Foerster , J. Links , H. -Q Zhou , A. Prestes Tonel , R. H. McKenzie

We study a one-dimensional lattice model of interacting spinless fermions. This model is integrable for both periodic and open boundary conditions, the latter case includes the presence of Grassmann valued non-diagonal boundary fields…

Mathematical Physics · Physics 2013-04-19 André M. Grabinski , Holger Frahm

Integrable sl(N) spin chains, which we consider in this paper, are not only the prototypical example of quantum integrable systems but also systems with a wide range of applications. For these models we use the Functional Separation of…

High Energy Physics - Theory · Physics 2022-11-30 Nikolay Gromov , Nicolo Primi , Paul Ryan

We introduce a universal framework for boundary transfer matrices, inspired by Sklyanin's two-row transfer matrix approach for quantum integrable systems with boundary conditions. The main examples arise from quantum symmetric pairs of…

Representation Theory · Mathematics 2025-10-22 Andrea Appel , Bart Vlaar

The analysis of the transfer matrices associated to the most general representations of the 8-vertex reflection algebra on spin-1/2 chains is here implemented by introducing a quantum separation of variables (SOV) method which generalizes…

Mathematical Physics · Physics 2015-06-16 S. Faldella , G. Niccoli

We refine the recently introduced notion of eclectic spin chains by including a maximal number of deformation parameters. These models are integrable, nearest-neighbor n-state spin chains with exceedingly simple non-hermitian Hamiltonians.…

High Energy Physics - Theory · Physics 2021-02-24 Changrim Ahn , Matthias Staudacher