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We use a groupoid model for the spin algebra to introduce boundary conditions on quantum spin systems via a Poisson point process representation. We can describe KMS states of quantum systems by means of a set of equations resembling the…
This article introduces the notion of good labellings for asymptotic lattices in order to study joint spectra of quantum integrable systems from the point of view of inverse spectral theory. As an application, we consider a new spectral…
Conventional methods of quantum simulation involve trade-offs that limit their applicability to specific contexts where their use is optimal. In particular, the interaction picture simulation has been found to provide substantial asymptotic…
In quantum mechanics, the connection between the operator algebraic realization and the logical models of measurement of state observables has long been an open question. In the approach that is presented here, we introduce a new…
We study the spectral statistics of quantum (metric) graphs whose vertices are equipped with preferred orientation vertex conditions. When comparing their spectral statistics to those predicted by suitable random matrix theory ensembles,…
A general graded reflection equation algebra is proposed and the corresponding boundary quantum inverse scattering method is formulated. The formalism is applicable to all boundary lattice systems where an invertible R-matrix exists. As an…
We study two-dimensional classically integrable field theory with independent boundary condition on each end, and obtain three possible generating functions for integrals of motion when this model is an ultralocal one. Classically…
In this article we review the basic concepts regarding quantum integrability. Special emphasis is given on the algebraic content of integrable models. The associated algebras are essentially described by the Yang-Baxter and boundary…
This work deals with the scattering entropy of quantum graphs in many different circumstances. We first consider the case of the Shannon entropy and then the R\'enyi and Tsallis entropies, which are more adequate to study distinct…
We consider quantum graphs with spin-orbit couplings at the vertices. Time-reversal invariance implies that the bond S-matrix is in the orthogonal or symplectic symmetry class, depending on spin quantum number s being integer or…
The density matrix of composite spin system is discussed in relation to the adjoint representation of unitary group U(n). The entanglement structure is introduced as an additional ingredient to the description of the linear space carrying…
Despite the apparent ubiquity and variety of quantum spin liquids in theory, experimental confirmation of spin liquids remains to be a huge challenge. Motivated by the recent surge of evidences for spin liquids in a series of candidate…
We present quantum complexity lower and upper bounds for independent set problems in graphs. In particular, we give quantum algorithms for computing a maximal and a maximum independent set in a graph. We present applications of these…
Borrowing ideas from the relation between simply laced Lie algebras and Dynkin diagrams, a weighted graph theory representation of quantum information is addressed. In this way, the density matrix of a quantum state can be interpreted as a…
In recent years, diagrammatic languages have been shown to be a powerful and expressive tool for reasoning about physical, logical, and semantic processes represented as morphisms in a monoidal category. In particular, categorical quantum…
Graphity models are characterized by configuration spaces in which states correspond to graphs and Hamiltonians that depend on local properties of graphs such as the degrees of vertices and numbers of short cycles. As statistical systems,…
A family of integrable $GL(NM)$ models is described. On the one hand it generalizes the classical spin Ruijsenaars--Schneider systems (the case $N=1$), and on the other hand it generalizes the relativistic integrable tops on $GL(N)$ Lie…
We present general mappings between classical spin systems and quantum physics. More precisely, we show how to express partition functions and correlation functions of arbitrary classical spin models as inner products between quantum…
State-of-the-art algorithms for simulating fermions coupled to gauge fields often rely on integrating fermion degrees of freedom. While successful in simulating QCD at zero chemical potential, at finite density these approaches are hindered…
Quantum graphs have recently emerged as models of nonlinear optical, quantum confined systems with exquisite topological sensitivity and the potential for predicting structures with an intrinsic, off-resonance response approaching the…