Related papers: Bethe ansatz and Hirota equation in integrable mod…
Recent developments in the theory of integrable models have provided the means of calculating dynamical correlation functions of some important observables in systems such as Heisenberg spin chains and one-dimensional atomic gases. This…
The T and Y-systems are ubiquitous structures in classical and quantum integrable systems. They are difference equations having a variety of aspects related to commuting transfer matrices in solvable lattice models, q-characters of…
We review the integrable structure of the Dirichlet boundary problem in two dimensions. The solution to the Dirichlet boundary problem for simply-connected case is given through a quasiclassical tau-function, which satisfies the Hirota…
This article is concerned with obtaining the standard tau function descriptions of integrable equations (in particular, here the KdV and Ernst equations are considered) from the geometry of their twistor correspondences. In particular, we…
For an arbitrary generalized quantum integrable spin chain we introduce a "master T -operator" which represents a generating function for commuting quantum transfer matrices constructed by means of the fusion procedure in the auxiliary…
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…
The Bethe Ansatz is a method that is used in quantum integrable models in order to solve them explicitly. This method is explained here in a general framework, which applies to 1D quantum spin chains, 2D statistical lattice models (vertex…
Exact non-perturbative partition functions of coupling constants and external fields exhibit huge hidden symmetry, reflecting the possibility to change integration variables in the functional integral. In many cases this implies also some…
Two different theoretical formulations of the finite temperature effects have been recently proposed for integrable field theories. In order to decide which of them is the correct one, we perform for a particular model an explicit check of…
We establish a series of integral formulae involving the Hurwitz zeta function. Applications are given to integrals of Bernoulli polynomials, log Gamma(q) and log sin(q).
Theta functions play a major role in many current researches and are powerful tools for studying integrable systems. The purpose of this paper is to provide a short and quick exposition of some aspects of meromorphic theta functions for…
Duality in the integrable systems arising in the context of Seiberg-Witten theory shows that their tau-functions indeed can be seen as generating functions for the mutually Poisson-commuting hamiltonians of the {\em dual} systems. We…
In the Thermodynamic Bethe Ansatz approach to 2D integrable, ADE-related quantum field theories one derives a set of algebraic functional equations (a Y-system) which play a prominent role. This set of equations is mapped into the problem…
We derive a set of bilinear functional equations of Hirota type for the partition functions of the $sl(2)$ related integrable statistical models defined on a random lattice. These equations are obtained as deformations of the Hirota…
The finite-volume thermodynamics of a massive integrable QFT is described in terms of a grand canonical ensemble of loops immersed in a torus and interacting through scattering factors associated with their intersections. The path integral…
We give a pedagogical introduction to the thermodynamic Bethe ansatz, a method that allows us to describe the thermodynamics of integrable models whose spectrum is found via the (asymptotic) Bethe ansatz. We set the stage by deriving the…
The integrable structure, recently revealed in some classical problems of the theory of functions in one complex variable, is discussed. Given a simply connected domain in the complex plane, bounded by a simple analytic curve, we consider…
We write down the functional equation of the zeta function of a global field. This equation is implicit in Weil's ``Basic Number Theory''.
An interpretation of Hirota bilinear relations for classical $\tau$ functions is given in terms of intertwining operators. Noncommutative example of $U_q(sl_2)$ is presented.
The thermodynamic Bethe ansatz (TBA) and the excited state TBA equations for an integrable spin chain related to the Lie superalgebra osp(1|2) are proposed by the quantum transfer matrix (QTM) method. We introduce the fusion hierarchy of…