Related papers: Functional Relations in Solvable Lattice Models I:…
We consider the $L$-state cyclic solid-on-solid lattice models under a class of open boundary conditions. The integrable boundary face weights are obtained by solving the reflection equations. Functional relations for the fused transfer…
We review and motivate recently-observed relationships between exactly solvable lattice models and modular representations of Hecke algebras. Firstly, we describe how the set of $n$-regular partitions label both of the following classes of…
We study a three dimensional Z(3)-symmetric effective theory of high temperature QCD. The exact lattice-continuum relations, needed in order to perform lattice simulations with physical parameters, are computed to order O(a^0) in lattice…
Extending the method proposed in [arXiv:1109.5524], we derive QQ-relations (functional relations among Baxter Q-functions) and T-functions (eigenvalues of transfer matrices) for fusion vertex models associated with the twisted quantum…
This book is mainly an exposition of the author's works and his joint works with his former students on explicit representations of finite-dimensional simple Lie algebras, related partial differential equations, linear orthogonal algebraic…
We propose a lattice density-functional theory for {\it ab initio} quantum chemistry or physics as a route to an efficient approach that approximates the full configuration interaction energy and orbital occupations for molecules with…
We study a three dimensional Z(3)-symmetric effective theory of high temperature QCD. The exact lattice-continuum relations, needed in order to perform lattice simulations with physical parameters, are computed to order O(a^0) in lattice…
These notes are based on a course given at the EPFL in May 2005. It is concerned with the representation theory of Hecke algebras in the non-semisimple case. We explain the role that these algebras play in the modular representation theory…
A new supersymmetric model for electrons with generalized hopping terms and Hubbard interaction on a one-dimensional lattice is solved by means of the Bethe Ansatz. We investigate the phase diagram of this model by studying the ground state…
We introduce the phase model on a lattice and solve it using the algebraic Bethe ansatz. Time-dependent temperature correlation functions of phase operators and the "darkness formation probability" are calculated in the thermodynamical…
We develop a method to give presentations of quantized function algebras of complex reductive groups. In particular, we give presentations of quantized function algebras of automorphism groups of finite dimensional simple complex Lie…
We consider a unitary circuit where the underlying gates are chosen to be R-matrices satisfying the Yang-Baxter equation and correlation functions can be expressed through a transfer matrix formalism. These transfer matrices are no longer…
Deformed exchange statistics is realized in terms of electronic operators. This is employed to rewrite Hubbard type lattice models for particles obeying deformed statistics (we refer to them as deformed models) as lattice models for…
In this work we obtain the exact solution of quantum integrable system associated with the Lie superalgebra $\mathfrak{gl}(1|1)$, both for periodic and for generic open boundary conditions. By means of the fusion technique we derive a…
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…
Braiding matrices in rational conformal field theory are considered. The braiding matrices for any two block four point function are computed, in general, using the holomorphic properties of the blocks and the holomorphic properties of…
A key objective in nuclear and high-energy physics is to describe nonequilibrium dynamics of matter, e.g., in the early universe and in particle colliders, starting from the Standard Model. Classical-computing methods, via the framework of…
We propose an approach to the problem of finite temperature dynamical correlation functions in integrable one-dimensional models with a spectral gap. The approach is based on the analysis of the singularities of the operator matrix elements…
We develop a transfer matrix method to compute exactly the spin-spin correlation functions of Bethe lattice spin models in the external magnetic field h and for any temperature T. We first compute the correlation function for the most…
We collect and systematize general definitions and facts on the application of quantum groups to the construction of functional relations in the theory of integrable systems. As an example, we reconsider the case of the quantum group…