Related papers: Integrable crosscap states in $\mathfrak{gl}(N)$ s…
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…
First, an algebraic criterion for integrability is discussed -the so-called `superintegrability'- and some results on the classification of superintegrable quantum spin Hamiltonians based on sl(2) are obtained. Next, the massive phases of…
We continue the survey initiated in arXiv:2012.14197 to explore the Bethe/Gauge correspondence between supersymmetric SO/Sp gauge theories in 2d/3d/4d and open spin chain with integrable boundaries. We collect the known Bethe ansatz…
We present the analytical Bethe ansatz for spin chains based on the superalgebras gl(M|N), $M\neq N$, with at each site an arbitrary representation (and including inhomogeneities). The calculation is done for closed and open spin chains. In…
We consider the case of an integrable quantum spin chain with "soliton non-peserving" boundary conditions. This is the first time that such boundary conditions have been considered in the spin chain framework. We construct the transfer…
We study the Blume-Emery-Griffiths spin glass model in presence of an attractive coupling between real replicas, and evaluate the effective potential as a function of the density overlap. We find that there is a region, above the first…
In this paper we discuss a family of models of particle and energy diffusion on a one-dimensional lattice, related to those studied previously in [Sasamoto-Wadati], [Barraquand-Corwin] and [Povolotsky] in the context of KPZ universality…
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…
Entanglement entropy has proven invaluable to our understanding of quantum criticality. It is natural to try to extend the concept to non-unitary quantum mechanics, which has seen growing interest from areas as diverse as open quantum…
We introduce a class of gapped Hamiltonians on quantum spin chains, which allows asymmetric edge ground states. This class is an asymmetric generalization of the class of Hamiltonians in [FNS]. It can be characterized by five qualitative…
Spin-liquid and spin-glass states represent two distinct phases of disordered quantum spin systems. These states are, in principle, distinguished by quantum-entangled fluctuations and spin freezing, but identifying each state and…
Central spin models describe a variety of quantum systems in which a spin-1/2 qubit interacts with a bath of surrounding spins, as realized in quantum dots and defect centers in diamond. We show that the fully anisotropic central spin…
Mixed states of samples of spin s particles which are symmetric under permutations of the particles are described in terms of their total collective spin quantum numbers. We use this description to analyze the influence on spin squeezing…
Several studies have exploited the integrable structure of central spin models to deepen understanding of these fundamental systems. In recent years, an underlying supersymmetry for systems with XX interactions has been uncovered. Here we…
Supersymmetry operators that change a spin chain's length have appeared in numerous contexts, ranging from the AdS/CFT correspondence to statistical mechanics models. In this article, we present, via an analysis of the Bethe equations, all…
The subject matter of this work is a 1D quantum spin - $\frac{1}{2}$ chain associated with the inhomogeneous six-vertex model possessing an additional ${\cal Z}_r$ symmetry. The model is studied in a certain parametric domain, where it is…
We propose a novel quantum integrable model for every non-simply laced simple Lie algebra ${\mathfrak g}$, which we call the folded integrable model. Its spectra correspond to solutions of the Bethe Ansatz equations obtained by folding the…
A coherent state of many spins contains quantum entanglement which increases with a decrease in the collective spin value. We present a scheme to engineer this class of pure state based on incoherent spin pumping with a few collective…
In this paper we clarify the relationship between inhomogeneous quantum spin chains and classical integrable many-body systems. It provides an alternative (to the nested Bethe ansatz) method for computation of spectra of the spin chains.…
We study the separability of permutationally symmetric quantum states. We show that for bipartite symmetric systems most of the relevant entanglement criteria coincide. However, we provide a method to generate examples of bound entangled…