Dynamics of thermalisation in small Hubbard-model systems

TL;DR

This paper investigates how small Hubbard-model systems thermalize over time, revealing that even tiny systems can reach equilibrium states through non-perturbative couplings, with relaxation dynamics differing from traditional perturbative predictions.

Contribution

It demonstrates that small Hubbard-model systems can thermalize via non-perturbative couplings, showing Gaussian relaxation and suggesting this behavior is generic for small quantum systems.

Findings

Subsystems reach equilibrium states even at small sizes

Relaxation to equilibrium is Gaussian in time under non-perturbative coupling

Behavior is consistent across different coupling types

Abstract

We study numerically the thermalisation and temporal evolution of the reduced density matrix for a two-site subsystem of a fermionic Hubbard model prepared far from equilibrium at a definite energy. Even for very small systems near quantum degeneracy, the subsystem can reach a steady state resembling equilibrium. This occurs for a non-perturbative coupling between the subsystem and the rest of the lattice where relaxation to equilibrium is Gaussian in time, in sharp contrast to perturbative results. We find similar results for random couplings, suggesting such behaviour is generic for small systems.