Related papers: Matrix-product operator dualities in integrable la…
We develop Yang-Baxter integrability structures connected with the quantum affine superalgebra Uq(\hat sl(2|1)). Baxter's Q-operators are explicitly constructed as supertraces of certain monodromy matrices associated with (q-deformed)…
Yang-Baxter (YB) map systems (or set-theoretic analoga of entwining YB structures) are presented. They admit zero curvature representations with spectral parameter depended Lax triples L1, L2, L3 derived from symplectic leaves of 2 x 2…
This work is based on the author's PhD thesis. The main result of the thesis is the use of the boost operator to develop a systematic method to construct new integrable spin chains with nearest-neighbour interaction and characterized by an…
We develop an approach for constructing the Baxter Q-operators for generic sl(N) spin chains. The key element of our approach is the possibility to represent a solution of the the Yang Baxter equation in the factorized form. We prove that…
Quantum computing is arguably one of the most revolutionary and disruptive technologies of this century. Due to the ever-increasing number of potential applications as well as the continuing rise in complexity, the development, simulation,…
We consider one dimensional block cellular automata, where the local update rules are given by Yang-Baxter maps, which are set theoretical solutions of the Yang-Baxter equations. We show that such systems are superintegrable: they possess…
Recently, there has been observed an interesting correspondence between supersymmetric quiver gauge theories with four supercharges and integrable lattice models of statistical mechanics such that the two-dimensional spin lattice is the…
We interpret values of spherical Whittaker functions on metaplectic covers of the general linear group over a nonarchimedean local field as partition functions of two different solvable lattice models. We prove the equality of these two…
Matrix orthogonal Laurent polynomials in the unit circle and the theory of Toda-like integrable systems are connected using the Gauss--Borel factorization of two, left and a right, Cantero-Morales-Velazquez block moment matrices, which are…
In the framework of the quantum inverse scattering method, we consider a problem of constructing local operators for two-dimensional quantum integrable models, especially for the lattice versions of the nonlinear Schrodinger and sine-Gordon…
Quantum tensor network states and more particularly projected entangled-pair states provide a natural framework for representing ground states of gapped, topologically ordered systems. The defining feature of these representations is that…
We show that infinite Matrix Product States (MPS) constructed from conformal field theories can describe ground states of one-dimensional critical systems with open boundary conditions. To illustrate this, we consider a simple infinite MPS…
Matrix product purifications (MPPs) are a very efficient tool for the simulation of strongly correlated quantum many-body systems at finite temperatures. When a system features symmetries, these can be used to reduce computation costs…
We use uniform matrix product states (MPS) to study the (1+1)D $O(2)$ and $O(4)$ rotor models, which are equivalent to the Kogut-Susskind formulation of matter-free nonabelian lattice gauge theory on a "hawaiian earring" graph for $U(1)$…
In this work, we prove that any element in the tensor product of separable infinite-dimensional Hilbert spaces can be expressed as a matrix product state (MPS) of possibly infinite bond dimension. The proof is based on the singular value…
Baxter's Q-operator is generally believed to be the most powerful tool for the exact diagonalization of integrable models. Curiously, it has hitherto not yet been properly constructed in the simplest such system, the compact spin-1/2…
This article concerns the MP inverse of the differences and the products of projections in a ring $R$ with involution. Some equivalent conditions are obtained. As applications, the MP invertibility of the commutator $pq-qp$ and the…
Loop braid groups characterize the exchange of extended objects, namely loops, in three dimensional space generalizing the notion of braid groups that describe the exchange of point particles in two dimensional space. Their interest in…
We study a quantum Yang-Baxter structure associated with non-ultralocal lattice models. We discuss the canonical structure of a class of integrable quantum mappings, i.e. canonical transformations preserving the basic commutation relations.…
We review recent progress on constructing non-equilibrium steady state density operators of boundary driven locally interacting quantum chains, where driving is implemented via Markovian dissipation channels attached to the chain's ends. We…