Abstract
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.
Highlights
In this work we have reported our findings for a search for Yang-Baxter integrable Lindblad equations
We have focused on translationally invariant situations where jump operators act on bonds or sites of a one dimensional chain
We have derived a superoperator representation for lattice models with both fermionic and bosonic degrees of freedom, and jump operators which can be bosonic or fermionic. In this representation the Lindblad equation takes the form of a imaginary time Schrödinger equation with a non-Hermitian “Hamiltonian” with local density, which can be thought of in terms of a two-leg ladder model of interacting spins or fermions
Summary
Weak couplings to an environment can have very interesting effects on the dynamics of manyparticle quantum systems In particular they can result in desirable non-equilibrium steady states [1,2,3,4,5]. While much progress has been made in analyzing Lindblad equations for many-particle systems by employing e.g. perturbative [11, 12] and matrix product states methods [13,14,15,16] it clearly is highly desirable to have exact solutions in specific, and hopefully representative, cases. Very recently examples of Lindblad equations with Liouvillians related to interacting Yang-Baxter integrable models have been found [27,28,29] This opens the door for bringing quantum integrability methods to bear on obtaining exact results for the dynamics of open many-particle quantum systems. In this work we report on the results of a search for integrable cases among a particular class of Lindblad equations for translationally invariant many-particle quantum systems
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