Related papers: Hidden E type structures in dilute A models
The fusion procedure of dilute $A_L$ models is constructed. It has been shown that the fusion rules have two types: $su(2)$ and $su(3)$. This paper is concerned with the $su(2)$ fusion rule mainly and the corresponding functional relations…
We present a one-dimensional multi-component model, known to be partially integrable when restricted to the subspaces made of only two components. By constructing fully anti-symmetrized bases, we find integrable excited eigenstates…
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 observe that the exactly solved eight-vertex solid-on-solid model contains an hitherto unnoticed arbitrary field parameter, similar to the horizontal field in the six-vertex model. The parameter is required to describe a continuous…
By interpreting the fusion matrix as an adjacency matrix we associate a loop model to every primary operator of a generic conformal field theory. The weight of these loop models is given by the quantum dimension of the corresponding primary…
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…
The Embedded-Atom Model (EAM) provides a phenomenological description of atomic arrangements in metallic systems. It consists of a configurational energy depending on atomic positions and featuring the interplay of two-body atomic…
We study the exact solutions of quantum integrable model associated with the $C_n$ Lie algebra, with either a periodic or an open one with off-diagonal boundary reflections, by generalizing the nested off-diagonal Bethe ansatz method.…
Recently, a new connection between density functional theory and kinetic theory has been proposed. In particular, it was shown that the Kohn-Sham (KS) equations can be reformulated as a macroscopic limit of the steady-state solution of a…
We review some surprising links which have been discovered in the last few years between the theory of certain ordinary differential equations, and particular integrable lattice models and quantum field theories in two dimensions. An…
This monograph introduces the reader to basic notions of integrable techniques for one-dimensional quantum systems. In a pedagogical way, a few examples of exactly solvable models are worked out to go from the coordinate approach to the…
Variable charge models (e.g., EEM, QEq, ES+) in reactive molecular dynamics simulations often inherently impose a global charge transfer between atoms (approximating each system as ideal metal). Consequently, most surface processes (e.g.,…
We use F-theory to classify possibly all six-dimensional superconformal field theories (SCFTs). This involves a two step process: We first classify all possible tensor branches allowed in F-theory (which correspond to allowed collections of…
Whereas the tools to determine the eigenvalues of the eight-vertex transfer matrix T are well known there has been until recently incomplete knowledge about the eigenvectors of T. We describe the construction of eigenvectors of T…
An analytic Bethe ansatz is carried out related to the type 1 Lie superalgebra C(s). We present eigenvalue formulae of transfer matrices in dressed vacuum form (DVF) labeled by Young superdiagrams with one row or one column. We also propose…
The last decade has witnessed an impressive progress in the theoretical understanding of transport properties of clean, one-dimensional quantum lattice systems. Many physically relevant models in one dimension are Bethe-ansatz integrable,…
Electron transfer (ET) at electrochemical interfaces is central to energy conversion and storage, yet its theoretical and computational modeling remain active research areas. This review elucidates key concepts and theories of ET kinetics,…
Zamolodchikov found an integrable field theory related to the Lie algebra E$_8$, which describes the scaling limit of the Ising model in a magnetic field. He conjectured that there also exist solvable lattice models based on E$_8$ in the…
The family of $A^{(1)}_2$ models on the square lattice includes a dilute loop model, a $15$-vertex model and, at roots of unity, a family of RSOS models. The fused transfer matrices of the general loop and vertex models are shown to satisfy…
Models of secluded dark matter offer a variant on the standard WIMP picture and can modify our expectations for hidden sector phenomenology and detection. In this work we extend a minimal model of secluded dark matter, comprised of a…