# Yang-Baxter integrable Lindblad equations

@article{Zikowska2020YangBaxterIL, title={Yang-Baxter integrable Lindblad equations}, author={Aleksandra Zi{\'o}łkowska and Fabian H. L. Essler}, journal={SciPost Physics}, year={2020} }

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.

## 23 Citations

### Constructing Integrable Lindblad Superoperators.

- Physics, MathematicsPhysical review letters
- 2021

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

- Mathematics, Physics
- 2022

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.

- Physics, MathematicsPhysical review. E
- 2020

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

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- 2022

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

- PhysicsJournal of Statistical Mechanics: Theory and Experiment
- 2021

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

- PhysicsProgress of Theoretical and Experimental Physics
- 2020

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

- Physics
- 2020

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

- PhysicsSciPost Physics
- 2022

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

- Physics, MathematicsJournal of Physics A: Mathematical and Theoretical
- 2020

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

- Physics, MathematicsPhysical Review Research
- 2022

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…

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