Related papers: Classical tau-function for quantum spin chains
The course of 5 lectures given at the seminar "Integrable Systems: from Classical to Quantum" (Universite de Montreal, Jul 26 -- Aug 6, 1999) contains a detailed comment on the recently discovered (Gaudin-Pasquier, 1992) connection between…
We construct new families of spin chain Hamiltonians that are local, integrable and translationally invariant. To do so, we make use of the Clifford group that arises in quantum information theory. We consider translation invariant Clifford…
Inspired by the integrable structures appearing in weakly coupled planar N=4 super Yang-Mills theory, we study Q-operators and Yangian invariants of rational integrable spin chains. We review the quantum inverse scattering method along with…
We use holography to compute the large-$N$ effective field theory along the moduli space of vacua of an infinite class of three-dimensional $\mathcal{N}=2$ SCFTs admitting a dual M-theory description. We focus in particular on toric models…
Generalized convolution symmetries of integrable hierarchies of KP and 2KP-Toda type multiply the Fourier coefficients of the elements of the Hilbert space $\HH= L^2(S^1)$ by a specified sequence of constants. This induces a corresponding…
We study a new generating functional of one-particle irreducible diagrams in quantum field theory, called master functional, which is invariant under the most general perturbative changes of field variables. The usual functional Gamma does…
We present a family of matrix models such that their partition functions are tau functions of the universal character (UC) hierarchy. This develops one of the topics of our previous paper arXiv:2410.14823. We found new matrix models…
The gl(N) and U_q(gl(N)) quantum spin chains in the presence of integrable spin impurities are considered. Within the Bethe ansatz formulation, we derive the associated transmission amplitudes, and the corresponding transmission matrices…
The general idea of this paper is to start from a classical integrable (partial differential) equation which arises as a compatibility condition for a matrix linear differential problem. For definitiveness' sake, a generalised sinh-Gordon…
We consider the question of what quantum spin chains naturally encode in their Hilbert space. It turns out that quantum spin chains are rather rich systems, naturally encoding solutions to various problems in combinatorics, group theory,…
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…
We derive spin operator matrix elements between general eigenstates of the superintegrable Z_N-symmetric chiral Potts quantum chain of finite length. Our starting point is the extended Onsager algebra recently proposed by R.Baxter. For each…
We propose an efficient grassmannian formalism for solution of bi-linear finite-difference Hirota equation (T-system) on T-shaped lattices related to the space of highest weight representations of $gl(K_1,K_2|M)$ superalgebra. The formalism…
We consider the quantum partition function for a system of quantum spinors and then derive an equivalent (or dual) classical partition function for some scalar degrees of freedom. The coupling between scalars is non-trivial (e.g. a model on…
We study operator mixing, due to planar one-loop corrections, for composite operators in D=4 supersymmetric theories. We present some N=1,2 Yang-Mills and Wess-Zumino models, in which the planar one-loop anomalous dimension matrix in the…
We demonstrate the surprising integrability of the classical Hamiltonian associated to a spin 1/2 system under periodic external fields. The one-qubit rotations generated by the dynamical evolution is, on the one hand, close to that of the…
This work, to be published in Transformation Groups in two parts, is devoted to the theory of nil-DAHA for the root system A_1 and its applications to symmetric and nonsymmetric (spinor) global q-Whittaker functions. These functions…
In this paper we investigate the tau-functions for the stationary sector of Gromov-Witten theory of the complex projective line and its version, relative to one point. In particular, we construct the integral representation for the points…
Using the free fermions technique and non-abelian bosonization rules we introduce the multi-component Pfaff-Toda hierarchy. The tau-function is defined as vacuum expectation value of a Clifford group element of the algebra of…
We present general mappings between classical spin systems and quantum physics. More precisely, we show how to express partition functions and correlation functions of arbitrary classical spin models as inner products between quantum…