Related papers: On a New Class of Integrable Models
We present an intuitive diagrammatic representation of a new class of integrable $\s$-models. It is shown that to any given diagram corresponds an integrable theory that couples $N$ WZW models with a certain number of each of the following…
This article is the first in a series devoted to computing the class groups of real quadratic fields. We present a new relation between the class number and the index of unit groups. This relation generalizes Hilbert class field theory for…
We construct new integrable systems describing particles with internal spin from four-dimensional $\mathcal{N}=2$ quiver gauge theories. The models can be quantized and solved exactly using the quantum inverse scattering method and also…
The aim of this paper is to survey some aspects of mapping class groups with focus on their finite dimensional representations arising in topological quantum field theory.
The notion of the genus of a quadratic form is generalized to vertex operator algebras. We define it as the modular braided tensor category associated to a suitable vertex operator algebra together with the central charge. Statements…
In this paper, we extend past work done on the application of the mathematics of category theory to quantum information science. Specifically, we present a realization of a dagger-compact category that can model finite-dimensional quantum…
Classical planar vertex models afford transfer matrices with real and positive entries, which makes this class of models suitable for quantum simulations. In this work, we support this statement by building explicit quantum circuits that…
Various aspects of the theory of quantum integrable systems are reviewed. Basic ideas behind the construction of integrable ultralocal and nonultralocal quantum models are explored by exploiting the underlying algebraic structures related…
New status in quantum mechanics is connected with recent achievements in the inverse problem. With its help instead of about ten exactly solvable models which serve as a basis of the contemporary education there are infinite (!) number,…
We consider quantum integrable models solvable by the nested algebraic Bethe ansatz and possessing $\mathfrak{gl}_3$-invariant $R$-matrix. We study a new recently proposed approach to construct on-shell Bethe vectors of these models. We…
We introduce a class of automorphisms of compact quantum groups which may be thought of as inner automorphisms and explore the behaviour of normal subgroups of compact quantum groups under these automorphisms. We also define the notion of…
Quantum-mechanical concepts can be formulated in constructive finite terms without loss of their empirical content if we replace a general unitary group by a unitary representation of a finite group. Any linear representation of a finite…
We characterize vertex algebras (in a suitable sense) as algebras over a certain graded co-operad. We also discuss some examples and categorical implications of this characterization.
In this paper we present a new procedure to obtain unitary and irreducible representations of Lie groups starting from the cotangent bundle of the group (the cotangent group). We discuss some applications of the construction in…
We propose a taxonomy for quantum algorithms grounded in the fundamental symmetries, both continuous and discrete, underlying quantum state spaces, oracles, and circuit dynamics. By organizing algorithms according to their symmetry groups…
In this paper we introduce the notion of admissible skein modules associated to an ideal in a pivotal category. We explain how these modules are generalizations of the Kauffman skein algebra and how they relate to renormalized quantum…
We construct some new Integrable Systems (IS) both classical and quantum associated with elliptic algebras. Our constructions are partly based on the algebraic integrability mechanism given by the existence of commuting families in skew…
We introduce the construction of induced corepresentations in the setting of locally compact quantum groups and prove that the resulting induced corepresentations are unitary under some mild integrability condition. We also establish a…
We study integrals of completely integrable quantum systems associated with classical root systems. We review integrals of the systems invariant under the corresponding Weyl group and as their limits we construct enough integrals of the…
Let G be a simple complex algebraic group. By using a notion of a G-category we define invariants of tangles with flat G-connections in their complements. We also show that quantized universal enveloping algebras at roots of unity provide…