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Functional relation for commuting quantum transfer matrices of quantum integrable models is identified with classical Hirota's bilinear difference equation. This equation is equivalent to the completely discretized classical 2D Toda lattice…

High Energy Physics - Theory · Physics 2019-08-15 I. Krichever , O. Lipan , P. Wiegmann , A. Zabrodin

The spectral curve is the key ingredient in the modern theory of classical integrable systems. We develop a construction of the ``quantum spectral curve'' and argue that it takes the analogous structural and unifying role on the quantum…

High Energy Physics - Theory · Physics 2007-05-23 A. Chervov , D. Talalaev

Applying braided Yang-Baxter equation quantum integrable and Bethe ansatz solvable 1D anyonic lattice and field models are constructed. Along with known models we discover novel lattice anyonic and $q$-anyonic models as well as nonlinear…

Exactly Solvable and Integrable Systems · Physics 2015-02-04 Anjan Kundu

Quantum systems on a one-dimensional lattice are ubiquitous in the study of models exactly-solved by Bethe Ansatz techniques. Here it is shown that including global-range interaction opens scope for Bethe Ansatz solutions that are not…

Exactly Solvable and Integrable Systems · Physics 2026-01-01 Jon Links

A quantum $n$-particle model consisting of an open $q$-difference Toda chain with two-sided boundary interactions is placed on a finite integer lattice. The spectrum and eigenbasis are computed by establishing the equivalence with a…

Mathematical Physics · Physics 2024-02-26 Jan Felipe van Diejen

Applying a unifying Lax operator approach to statistical systems a new class of integrable vertex models based on quantum algebra is proposed, which exhibits a rich variety for generic q, q roots of unity and q -> 1. Exact solutions are…

Condensed Matter · Physics 2009-11-07 Anjan Kundu

Correlation functions of quantum systems -- central objects in quantum field theories -- are defined in high-dimensional space-time domains. Their numerical treatment thus suffers from the curse of dimensionality, which hinders the…

Strongly Correlated Electrons · Physics 2023-05-01 Hiroshi Shinaoka , Markus Wallerberger , Yuta Murakami , Kosuke Nogaki , Rihito Sakurai , Philipp Werner , Anna Kauch

We apply the algebraic Bethe ansatz developed in our previous paper \cite{CM} to three different families of U(1) integrable vertex models with arbitrary $N$ bond states. These statistical mechanics systems are based on the higher spin…

Mathematical Physics · Physics 2009-08-03 M. J. Martins , C. S. Melo

We propose a set of algebraic equations describing eigenvalues and eigenstates of a relativistic evolution operator for a two-dimensional $q$-oscillator Kagom\'e lattice. Evolution operator is constructed with the help of $q$-oscillator…

Mathematical Physics · Physics 2026-01-01 Sergey Sergeev

Analog quantum simulation has the potential to be an indispensable technique in the investigation of complex quantum systems. In this work, we numerically investigate a one-dimensional, faithful, analog, quantum electronic circuit simulator…

Quantum Physics · Physics 2021-06-03 Ananda Roy , Dirk Schuricht , Johannes Hauschild , Frank Pollmann , Hubert Saleur

In this work we revisit the problem of the quantization of the two-dimensional O(3) non-linear sigma model and its one-parameter integrable deformation -- the sausage model. Our consideration is based on the so-called ODE/IQFT…

High Energy Physics - Theory · Physics 2018-02-14 Vladimir V. Bazhanov , Gleb A. Kotousov , Sergei L. Lukyanov

Some features of integrable lattice models are reviewed for the case of the six-vertex model. By the Bethe ansatz method we derive the free energy of the six-vertex model. Then, from the expression of the free energy we show analytically…

Statistical Mechanics · Physics 2007-05-23 Tetsuo Deguchi

We propose a model for the quantum harmonic oscillator on a discrete lattice which can be written in supersymmetric form, in contrast with the more direct discretization of the harmonic oscillator. Its ground state is easily found to be…

Quantum Physics · Physics 2015-05-30 Manuel Valiente

We have recently constructed a large class of open quantum spin chains which have quantum-algebra symmetry and which are integrable. We show here that these models can be exactly solved using a generalization of the analytical Bethe Ansatz…

High Energy Physics - Theory · Physics 2014-11-18 Luca Mezincescu , Rafael I. Nepomechie

In this paper we investigate an integrable loop model and its connection with a supersymmetric spin chain. The Bethe Ansatz solution allows us to study some properties of the ground state. When the loop fugacity $q$ lies in the physical…

Statistical Mechanics · Physics 2009-10-30 M. J. Martins , B. Nienhuis , R. Rietman

In this article we review the basic concepts regarding quantum integrability. Special emphasis is given on the algebraic content of integrable models. The associated algebras are essentially described by the Yang-Baxter and boundary…

Mathematical Physics · Physics 2010-09-29 Anastasia Doikou , Stefano Evangelisti , Giovanni Feverati , Nikos Karaiskos

Quantum computers are ideally set up to solve linear systems which are of a form similar to the Schrodinger/Dirac equation of quantum mechanics. In the framework of linear response theory, the propagation and scattering of electromagnetic…

We recognize quantum circuit model of computation as factorisable scattering model and propose that a quantum computer is associated with a quantum many-body system solved by the Bethe ansatz. As an typical example to support our…

General Physics · Physics 2012-04-10 Yong Zhang

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 introduce the notions of $(G,q)$-opers and Miura $(G,q)$-opers, where $G$ is a simply-connected complex simple Lie group, and prove some general results about their structure. We then establish a one-to-one correspondence between the set…

Algebraic Geometry · Mathematics 2026-04-06 Edward Frenkel , Peter Koroteev , Daniel S. Sage , Anton M. Zeitlin