Abstract
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 operator-space fragmentation and each block is Yang–Baxter integrable. For particular loss/gain rates the model can be mapped to free fermions. We determine the full quantum dynamics for an initial product state in this case.
Highlights
Whilst most standard tools for many-body quantum mechanics only apply to closed systems, real systems are invariably influenced by their environment
Given that solvable models have provided deep insights into the non-equilibrium dynamics of closed many body systems [11, 12, 13, 14] it is natural to ask if there are any exact results that can be obtained for many particle Lindblad equations
A new direction for constructing solvable many particle Lindblad equations was identified through the discovery of Lindblad equations that can be related to interacting Yang-Baxter integrable models [34, 35, 36, 37, 38, 32, 33, 39, 40, 41, 42]
Summary
Whilst most standard tools for many-body quantum mechanics only apply to closed systems, real systems are invariably influenced by their environment. A characteristic feature of these models is the fundamental boson or fermion operators fulfil linear equations of motion and concomitantly so do the Green’s functions of interest Another step towards obtaining exact solutions of many particle Lindblad equations was the discovery that there exist classes of models in which some or all local correlation functions satisfy closed hierarchies of equations of motion [24, 25, 26, 27, 28, 29, 30]. It is based on a “fragmentation” of the space of operators into an exponential (in system size) number of subspaces that are left invariant under the dissipative evolution This mechanism applies to the quantum version of the simple asymmetric exclusion process (ASEP) [44, 45, 46, 47]. We relegate some technical calculations necessary for the conclusions in the main text to two appendices
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