Closed and Open System Dynamics in a Fermionic Chain with a Microscopically Specified Bath: Relaxation and Thermalization

TL;DR

This paper investigates how a one-dimensional fermionic chain coupled to baths thermalizes over time, revealing prethermalization and full thermalization behaviors depending on density and coupling strength.

Contribution

It introduces a detailed study of thermalization dynamics in a fermionic chain with microscopically specified baths, combining numerical methods and analytical descriptions.

Findings

Prethermalization occurs at intermediate times for higher densities.

Full thermalization to grand canonical ensemble at long times.

Fermi momentum distribution observed in equilibrium despite simplified bath model.

Abstract

We study thermalization in a one-dimensional quantum system consisting of a noninteracting fermionic chain with each site of the chain coupled to an additional bath site. Using a density matrix renormalization group algorithm we investigate the time evolution of observables in the chain after a quantum quench. For low densities we show that the intermediate time dynamics can be quantitatively described by a system of coupled equations of motion. For higher densities our numerical results show a prethermalization for local observables at intermediate times and a full thermalization to the grand canonical ensemble at long times. For the case of a weak bath-chain coupling we find, in particular, a Fermi momentum distribution in the chain in equilibrium in spite of the seemingly oversimplified bath in our model.