Real-Time Evolution of Strongly Coupled Fermions driven by Dissipation

TL;DR

This paper studies the real-time dynamics of strongly coupled lattice fermions under dissipation, revealing exponential decay of order parameters and momentum-dependent relaxation rates through solvable differential equations.

Contribution

It introduces a framework for analyzing dissipative evolution of strongly coupled fermions using Lindblad operators, with exact solutions for two-point functions.

Findings

Exponential decay of the staggered occupation order parameter.

Slowing down of low-momentum modes due to particle number conservation.

Decay rates proportional to lattice coordination number.

Abstract

We consider the real-time evolution of a strongly coupled system of lattice fermions whose dynamics is driven entirely by dissipative Lindblad processes, with linear or quadratic quantum jump operators. The fermion 2-point functions obey a closed set of differential equations, which can be solved with linear algebra methods. The staggered occupation order parameter of the t-V model decreases exponentially during the dissipative time evolution. The structure factor associated with the various Fourier modes shows the slowing down of low-momentum modes, which is due to particle number conservation. The processes with nearest-neighbor-dependent Lindblad operators have a decay rate that is proportional to the coordination number of the spatial lattice.