Related papers: Models with Quantum Symmetry and their Spectra
It is shown that the symmetry algebra of quantum superintegrable system can be always chosen to be u(N),N being the number of degrees of freedom.
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…
We systematise and develop a graphical approach to the investigations of quantum integrable vertex statistical models and the corresponding quantum spin chains. The graphical forms of the unitarity and various crossing relations are…
We present a construction of integrable quantum spin chains where local spin-spin interactions are weighted by ``position''-dependent potential containing abelian non-local spin dependance. This construction applies to the previously…
We study the ring theory of the multiparameter deformations of the quantum Schubert cell algebras obtained from 2-cocycle twists. This is a large family, which extends the Artin-Schelter-Tate algebras of twisted quantum matrices. We…
In the correspondence between spectral problems and topological strings, it is natural to consider complex values for the string theory moduli. In the spectral theory side, this corresponds to non-Hermitian quantum curves with complex…
This paper addresses the three following questions. (i) How the structures of group and of chain of groups enter nuclear, atomic and molecular spectroscopy? (ii) How these structures can be exploited, in a quantum- mechanical framework, in…
We consider a class of ground states for quantum spin chains on an integer lattice. First we show that presence of the spectral gap between the ground state energy and the rest of spectrum implies the split property of certain subsystems.As…
This note is a review of the recently revealed intriguing connection between integrable quantum spin chains and integrable many-body systems of classical mechanics. The essence of this connection lies in the fact that the spectral problem…
Usually quantum chains with quantum group symmetry are associated with representations of quantized universal algebras $U_q(g) $ . Here we propose a method for constructing quantum chains with $C_q(G)$ global symmetry , where $C_q(G)$ is…
A general way to construct chain models with certain Lie algebraic or quantum Lie algebraic symmetries is presented. These symmetric models give rise to series of integrable systems. As an example the chain models with $A_n$ symmetry and…
The paper intends to lay out the first steps towards constructing a unified framework to understand the symplectic and spectral theory of finite dimensional integrable Hamiltonian systems. While it is difficult to know what the best…
We examine a simple heuristic test of integrability for quantum chains. This test is applied to a variety of systems, including a generic isotropic spin-1 model with nearest-neighbor interactions and a multiparameter family of spin-1/2…
What can one do with a given tunable quantum device? We provide complete symmetry criteria deciding whether some effective target interaction(s) can be simulated by a set of given interactions. Symmetries lead to a better understanding of…
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,…
A general algebraic approach, incorporating both invariance groups and dynamic symmetry algebras, is developed to reveal hidden coherent structures (closed complexes and configurations) in quantum many-body physics models due to symmetries…
The general expression for the local matrix $L(\theta)$ of a quantum chain with the site space in any representation of $su(3)$ is obtained. This is made by generalizing $L(\theta)$ from the fundamental representation and imposing the…
The interplay between supersymmetry and classical and quantum computation is discussed. First, it is shown that the problem of computing the Witten index of $\mathcal N \leq 2$ quantum mechanical systems is $\#P$-complete and therefore…
Quantum spin chains are prototype quantum many-body systems. They are employed in the description of various complex physical phenomena. The goal of this paper is to provide an introduction to the subject by focusing on the time evolution…
We introduce and motivate the study of quantum spin chains on a one-dimensional lattice. We classify the varieties of methods that have been used to study these models into three categories, - a) exact methods to study specific models b)…