Thermalisation of Local Observables in Small Hubbard Lattices

TL;DR

This paper investigates how small Hubbard lattice systems thermalize, showing that interactions and system parameters influence thermalization, supported by numerical and theoretical analysis related to the eigenstate thermalization hypothesis.

Contribution

It provides a detailed numerical and theoretical analysis of thermalization in small Hubbard lattices, emphasizing the role of interactions and finite-size effects.

Findings

Thermalization occurs over a wide parameter range.

Interactions are essential for efficient thermalization.

Finite-size scaling aligns with random matrix theory predictions.

Abstract

We present a study of thermalisation of a small isolated Hubbard lattice cluster prepared in a pure state with a well-defined energy. We examine how a two-site subsystem of the lattice thermalises with the rest of the system as its environment. We explore numerically the existence of thermalisation over a range of system parameters, such as the interaction strength, system size and the strength of the coupling between the subsystem and the rest of the lattice. We find thermalisation over a wide range of parameters and that interactions are crucial for efficient thermalisation of small systems. We relate this thermalisation behaviour to the eigenstate thermalisation hypothesis and quantify numerically the extent to which eigenstate thermalisation holds. We also verify our numerical results theoretically with the help of previously established results from random matrix theory for the local density of states, particularly the finite-size scaling for the onset of thermalisation.