Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Communications in Mathematical Physics

Quantum discrete sine-Gordon model at roots of 1: Integrable quantum system on the integrable classical background

Vladimir V. Bazhanov, Александр Иванович Бобенко, Nicolai Reshetikhin

Published Jan 1, 1996• 40 citations
Publisher
DOI
10.1007/bf02102413

Related papers

Exact form factors in integrable quantum field theories: the sine-Gordon model (II)

H. Babujian, M. Karowski

arXiv:hep-th/0105178•Nuclear Physics B•Jan 1, 2002•92 citations

Quantum Integrable Models on 1 + 1 Discrete Space Time

L. D. Faddeev, A. Yu. Volkov

NATO ASI series. Series B : Physics•Jan 1, 1997•3 citations

Chiral Potts model and the discrete Sine-Gordon model at roots of unity

Vladimir V. Bazhanov

<!-- *** Custom HTML *** --> The discrete quantum Sine-Gordon model at roots of unity remarkably combines a classical integrable system with an integrable quantum spin system, whose parameters obey classical equations of motion. We show that the fundamental $R$-matrix of the model (which satisfies a difference property Yang–Baxter equation) naturally splits into a product of a singular "classical" part and a finite dimensional quantum part. The classical part of the $R$-matrix itself satisfies the quantum Yang–Baxter equation, and therefore can be factored out producing, however, a certain "twist" of the quantum part. We show that the resulting equation exactly coincides with the star-triangle relation of the $N$-state chiral Potts model. The associated spin model on the whole lattice is, in fact, more general than the chiral Potts and reduces to the latter only for the simplest (constant) classical background. In a general case the model is inhomogeneous: its Boltzmann weights are determined by non-trivial background solutions of the equations of motion of the classical discrete sine-Gordon model.

arXiv:0809.2351•Advanced studies in pure mathematics•Mar 7, 2019•9 citations

Free massive fermions inside the quantum discrete sine-Gordon model

N. Kutz, Technische Univ. Berlin (Germany). Sonderforschungsbereich 288 -Differentialgeometrie und Quantenphysik

We extend the notion of space shifts introduced in [FV3] for certain quantum light cone lattice equations of sine-Gordon type at root of unity (e.g. [FV1][FV2][BKP][BBR]). As a result we obtain a compatibility equation for the roots of central elements within the algebra of observables (also called current algebra). The equation which is obtained by exponentiating these roots is exactly the evolution equation for the "classical background" as described in [BBR]. As an application for the introduced constructions, a one to one correspondence between a special case of the quantum light cone lattice equations of sine-Gordon type and free massive fermions on a lattice as constructed in [DV] is derived. Supported by the Deutsche Forschungsgemeinschaft, Sonderforschungsbereich 288 e-mail: nadja@math.tu-berlin.de 1 Introduction Let us consider a class of integrable lattice systems defined by an evolution equation of the following type: g u = V 0 (g l \\Gamma g r ) + g d = 0; (1) where...

•Jan 1, 1996•1 citation

Quantum Integrable Systems on a Classical Integrable Background

Andrii Nikolaevich Liashyk, Nicolai Reshetikhin, Ivan Andreevich Sechin

arXiv:2405.17865•Communications in Mathematical Physics•Dec 8, 2025•4 citations

The Quantum Volterra Model and the Lattice Sine–Gordon System. – Construction of the BaxterQOperator and the Integrals of Motion

Kazuhiro Hikami, Rei Inoue

We investigate the integrable structure of the quantum Volterra model, which is a discretization of the Korteweg–de Vries equation. Based on Sklyanin's method we derive the Baxter equation, and then clarify a role of the “fundamental transfer matrix”. We show that the fundamental transfer matrix also generates the integrals of motion for a lattice analogue of the sine–Gordon system.

Journal of the Physical Society of Japan•Feb 15, 1999•0 citations
<!-- *** Custom HTML *** --> The discrete quantum Sine-Gordon model at roots of unity remarkably combines a classical integrable system with an integrable quantum spin system, whose parameters obey classical equations of motion. We show that the fundamental RRR-matrix of the model (which satisfies a difference property Yang–Baxter equation) naturally splits into a product of a singular "classical" part and a finite dimensional quantum part. The classical part of the RRR-matrix itself satisfies the quantum Yang–Baxter equation, and therefore can be factored out producing, however, a certain "twist" of the quantum part. We show that the resulting equation exactly coincides with the star-triangle relation of the NNN-state chiral Potts model. The associated spin model on the whole lattice is, in fact, more general than the chiral Potts and reduces to the latter only for the simplest (constant) classical background. In a general case the model is inhomogeneous: its Boltzmann weights are determined by non-trivial background solutions of the equations of motion of the classical discrete sine-Gordon model.
We extend the notion of space shifts introduced in [FV3] for certain quantum light cone lattice equations of sine-Gordon type at root of unity (e.g. [FV1][FV2][BKP][BBR]). As a result we obtain a compatibility equation for the roots of central elements within the algebra of observables (also called current algebra). The equation which is obtained by exponentiating these roots is exactly the evolution equation for the "classical background" as described in [BBR]. As an application for the introduced constructions, a one to one correspondence between a special case of the quantum light cone lattice equations of sine-Gordon type and free massive fermions on a lattice as constructed in [DV] is derived. Supported by the Deutsche Forschungsgemeinschaft, Sonderforschungsbereich 288 e-mail: nadja@math.tu-berlin.de 1 Introduction Let us consider a class of integrable lattice systems defined by an evolution equation of the following type: g u = V 0 (g l \\Gamma g r ) + g d = 0; (1) where...