Related papers: Yang-Baxter integrable Lindblad equations

We present an "algebraic treatment" of the analytical Bethe Ansatz. For this purpose, we introduce abstract monodromy and transfer matrices which provide an algebraic framework for the analytical Bethe Ansatz. It allows us to deal with a…

We propose that Baxter's Z-invariant six-vertex model at the rational gl(2) point on a planar but in general not rectangular lattice provides a way to study Yangian invariants. These are identified with eigenfunctions of certain monodromies…

The algebraic Bethe ansatz is a powerful method to diagonalize transfer-matrices of statistical models derived from solutions of (graded) Yang Baxter equations, connected to fundamental representations of Lie (super-)algebras and their…

We construct novel solutions to the set-theoretical entwining Yang-Baxter equation. These solutions are birational maps involving non-commutative dynamical variables which are elements of the Grassmann algebra of order $n$. The maps arise…

Time-dependent Lindblad master equations have important applications in areas ranging from quantum thermodynamics to dissipative quantum computing. In this paper we outline a general method for writing down exact solutions of time-dependent…

We present a canonical derivation of an influence superoperator which generates the reduced dynamics of a Fermionic quantum system linearly coupled to a Fermionic environment initially at thermal equilibrium. We use this formalism to derive…

A brief non-technical review of the recent study of classical integrable structures in quantum integrable systems is given. It is explained how to identify the standard objects of quantum integrable systems (transfer matrices, Baxter's…

This topical review article reports rapid progress on the generalization and application of entanglement in non-Hermitian free-fermion quantum systems. We begin by examining the realization of non-Hermitian quantum systems through the…

We introduce non-degenerate solutions of the Yang-Baxter equation in the setting of symmetric monoidal categories. Our theory includes non-degenerate set-theoretical solutions as basic examples. However, infinite families of non-degenerate…

This paper considers aspects of a Kagome lattice system with states classified by plane partitions. Using two sets of free fermions, we rewrite the lattice in terms of two families of spin chains. In this formalism, the quantum crystals…

We show that the one dimensional, critical transverse field Ising model is Yang-Baxter integrable. This is done by constructing commuting transfer matrices built out of a $R$-matrix satisfying the Yang-Baxter equation with additive spectral…

Several years ago, it was proposed that the usual solutions of the Yang-Baxter equation associated to Lie groups can be deduced in a systematic way from four-dimensional gauge theory. In the present paper, we extend this picture, fill in…

We investigate the dissipative dynamics yielded by the Lindblad equation within the coexistence region around a first order phase transition. In particular, we consider an exactly-solvable fullyconnected quantum Ising model with n-spin…

By employing the Lindblad equation, we derive the evolution of the two-point correlator for a free-fermion chain of length $L$ subject to bulk dephasing and boundary losses. We use the Bethe ansatz to diagonalize the Liouvillian ${\mathcal…

We consider the case of an integrable quantum spin chain with ``soliton non-preserving'' boundary conditions. This is the first time that such boundary conditions have been considered in the spin chain framework. We construct the transfer…

The Bethe ansatz equations of the fundamental Sp(2N) integrable model are solved by a peculiar configuration of roots leading us to determine the nature of the excitations. They consist of N elementary generalized spinons and N-1 composite…

New classes of integrable boundary conditions for the q-deformed (or two-parameter) supersymmetric U model are presented. The boundary systems are solved by using the coordinate space Bethe ansatz technique and Bethe ansatz equations are…

We consider involutive, non-degenerate, finite set theoretic solutions of the Yang-Baxter equation. Such solutions can be always obtained using certain algebraic structures that generalize nil potent rings called braces. Our main aim here…

In this paper we review the theory of the Yang-Baxter equation related to the 6-vertex model and its higher spin generalizations. We employ a 3D approach to the problem. Starting with the 3D R-matrix, we consider a two-layer projection of…

Quadratic systems generated using Yang-Baxter equations are integrable in a sense, but we display a deterioration in the possession of the Painlev\'e property as the number of equations in each `integrable system' increases. Certain…