Results 1 to 10 of about 894 (262)

Branes and integrable lattice models [PDF]

Modern Physics Letters A, 2017
This is a brief review of my work on the correspondence between four-dimensional [Formula: see text] supersymmetric field theories realized by brane tilings and two-dimensional integrable lattice models. I explain how to construct integrable lattice models from extended operators in partially topological quantum field theories, and elucidate the ...
Junya Yagi
exaly   +4 more sources

Correlation Functions for Lattice Integrable Models

Acta Polytechnica, 2008
In this lectures I consider the problem of calculating the correlation functions for XXZ spin chain. First, I explain in details the free fermion case.
F. Smirnov
doaj   +3 more sources

Integrable Lattice Spin Models from Supersymmetric Dualities [PDF]

Physics of Particles and Nuclei Letters, 2018
Recently, there has been observed an interesting correspondence between supersymmetric quiver gauge theories with four supercharges and integrable lattice models of statistical mechanics such that the two-dimensional spin lattice is the quiver diagram, the partition function of the lattice model is the partition function of the gauge theory and the ...
Ilmar Gahramanov, Shahriyar Jafarzade
exaly   +4 more sources

Quiver gauge theories and integrable lattice models [PDF]

Journal of High Energy Physics, 2015
We discuss connections between certain classes of supersymmetric quiver gauge theories and integrable lattice models from the point of view of topological quantum field theories (TQFTs). The relevant classes include 4d $\mathcal{N} = 1$ theories known as brane box and brane tilling models, 3d $\mathcal{N} = 2$ and 2d $\mathcal{N} = (2,2)$ theories ...
Junya Yagi
exaly   +4 more sources

Generalized Gibbs ensemble in integrable lattice models [PDF]

Journal of Statistical Mechanics: Theory and Experiment, 2016
Abstract The generalized Gibbs ensemble (GGE) was introduced ten years ago to describe observables in isolated integrable quantum systems after equilibration. Since then, the GGE has been demonstrated to be a powerful tool to predict the outcome of the relaxation dynamics of few-body observables in a variety of integrable models, a ...
Marcos Rigol, Lev Vidmar
exaly   +4 more sources

Branes and categorifying integrable lattice models [PDF]

Advances in Theoretical and Mathematical Physics, 2020
19 pp. Minor improvements and typos corrected.
Ashwinkumar, Meer, Tan, Meng-Chwan, Zhao, Qin   +2 more
openaire   +2 more sources

Integrable lattice models and holography [PDF]

Journal of High Energy Physics, 2021
AbstractWe study four-dimensional Chern-Simons theory onD ×ℂ (whereDis a disk), which is understood to describe rational solutions of the Yang-Baxter equation from the work of Costello, Witten and Yamazaki. We find that the theory is dual to a boundary theory, that is a three-dimensional analogue of the two-dimensional chiral WZW model.
openaire   +2 more sources

Integrability for multidimensional lattice models [PDF]

Physics Letters B, 1989
Abstract The generating principle for the algebraic construction of the hierarchy of the d-simplex equations generalizing the Yang-Baxter equation in any dimension d is given. Following this principle, we construct the generalization of the Lax equations for multidimensional integrable systems.
Jean Michel Maillet, Frank Nijhoff
openaire   +1 more source

Solution of tetrahedron equation and cluster algebras

Journal of High Energy Physics, 2021
We notice a remarkable connection between the Bazhanov-Sergeev solution of Zamolodchikov tetrahedron equation and certain well-known cluster algebra expression. The tetrahedron transformation is then identified with a sequence of four mutations.
P. Gavrylenko, M. Semenyakin, Y. Zenkevich   +2 more
doaj   +1 more source

NEW SERIES OF 3D LATTICE INTEGRABLE MODELS [PDF]

International Journal of Modern Physics A, 1994
In this paper we present a new series of three-dimensional integrable lattice models with N colors. The case N=2 generalizes the elliptic model of Ref. 8. The weight functions of the models satisfy modified tetrahedron equations with N states and give a commuting family of two-layer transfer matrices.
Mangazeev, V. V., Sergeev, S. M., Stroganov, Yu. G.   +2 more
openaire   +2 more sources