Yang-Baxter integrable Lindblad equations

  title={Yang-Baxter integrable Lindblad equations},
  author={Aleksandra Zi{\'o}łkowska and Fabian H. L. Essler},
  journal={SciPost Physics},
We consider Lindblad equations for one dimensional fermionic models and quantum spin chains. By employing a (graded) super-operator formalism we identify a number of Lindblad equations than can be mapped onto non-Hermitian interacting Yang-Baxter integrable models. Employing Bethe Ansatz techniques we show that the late-time dynamics of some of these models is diffusive. 

Constructing Integrable Lindblad Superoperators.

A new method is developed for the construction of one-dimensional integrable Lindblad systems, which describe quantum many body models in contact with a Markovian environment and establishes a structured approach to the study of solvable open quantum systems.

The Bethe ansatz for a new integrable open quantum system

In this paper we apply the nested algebraic Bethe ansatz to compute the eigenvalues and the Bethe equations of the transfer matrix of the new integrable Lindbladian found in [1]. We show that it can

Integrability of one-dimensional Lindbladians from operator-space fragmentation.

We introduce families of one-dimensional Lindblad equations describing open many-particle quantum systems that are exactly solvable in the following sense: (i) The space of operators splits into

The Floquet Baxterisation

Quantum integrability has proven to be a useful tool to study quantum many-body systems out of equilibrium. In this paper we construct a generic framework for integrable quantum circuits through the

Exact solution of a quantum asymmetric exclusion process with particle creation and annihilation

We consider a Lindblad equation that for particular initial conditions reduces to an asymmetric simple exclusion process with additional loss and gain terms. The resulting Lindbladian exhibits

Quantum Ising chain with boundary dephasing

We study the quantum Ising chain with boundary dephasing. By doubling the Hilbert space, the model is mapped to the Su–Schrieffer–Heeger model with imaginary chemical potential at the edges. We

Integrable nonunitary open quantum circuits

We explicitly construct an integrable interacting dissipative quantum circuit, via a trotterization of the Hubbard model with imaginary interaction strength. To prove integrability, we build an

Dynamics of fluctuations in quantum simple exclusion processes

We consider the dynamics of fluctuations in the quantum asymmetric simple exclusion process (Q-ASEP) with periodic boundary conditions. The Q-ASEP describes a chain of spinless fermions with random

Trigonometric SU(N) Richardson–Gaudin models and dissipative multi-level atomic systems

We derive the exact solution of a system of N-level atoms in contact with a Markovian reservoir. The resulting Liouvillian expressed in a vectorized basis is mapped to an SU(N) trigonometric

Dissipative dynamics in open XXZ Richardson-Gaudin models

In specific open systems with collective dissipation the Liouvillian can be mapped to a non-Hermitian Hamiltonian. We here consider such a system where the Liouvillian is mapped to an XXZ



Fermionic representations of integrable lattice systems

We develop a general scheme for the use of Fermi operators within the framework of integrable systems. This enables us to read off a fermionic Hamiltonian from a given solution of the Yang-Baxter

Exact Integrability of the su(n) Hubbard Model

The bosonic su(n) Hubbard model was recently introduced. The model was shown to be integrable in one dimension by exhibiting the infinite set of conserved quantities. I derive the R-matrix and use it

Infinite conservation laws in the one-dimensional Hubbard model.

  • Shastry
  • Physics, Mathematics
    Physical review letters
  • 1986
It is shown that the Hamiltonian of the 1D Hubbard model commutes with a one-parameter family of transfer matrices of a new 2D classical model corresponding to two coupled six-vertex models, a generalization of the (infinitesimal) startriangle relation.

Including a phase in the Bethe equations of the Hubbard model

We compute the Bethe equations of generalized Hubbard models, and study their thermodynamical limit. We argue how they can be connected to the ones found in the context of AdS/CFT correspondence, in

Third quantization: a general method to solve master equations for quadratic open Fermi systems

The Lindblad master equation for an arbitrary quadratic system of n fermions is solved explicitly in terms of diagonalization of a 4n×4n matrix, provided that all Lindblad bath operators are linear

Solutions of the Yang-Baxter equation

We give the basic definitions connected with the Yang-Baxter equation (factorization condition for a multiparticle S-matrix) and formulate the problem of classifying its solutions. We list the known

Integrable graded magnets

Solutions of the graded Yang-Baxter equations are constructed which are invariant relative to the general linear and orthosymplectic supergroups. The Hamiltonians and other higher integrals (the

Fermionic R-Operator and Integrability of the One-Dimensional Hubbard Model

We propose a new type of the Yang-Baxter equation (YBE) and the decorated Yang-Baxter equation (DYBE). Those relations for the fermionic R -operator were introduced recently as a tool to treat the