Thermalization rates in the one dimensional Hubbard model with next-to-nearest neighbor hopping

TL;DR

This paper investigates how next-to-nearest neighbor hopping influences thermalization rates in a one-dimensional Hubbard model, revealing a quadratic dependence and exponential temperature effects.

Contribution

It demonstrates that even weak next-to-nearest neighbor hopping induces thermalization, with rates proportional to the square of the hopping amplitude, using a quantum Boltzmann equation approach.

Findings

Thermalization rates are proportional to the square of the next-to-nearest neighbor hopping.

Thermalization occurs even with weak next-to-nearest neighbor hopping.

Rates become exponentially small at low temperatures away from half filling.

Abstract

We consider a fermionic Hubbard chain with an additional next-to-nearest neighbor hopping term. We study the thermalization rates of the quasi-momentum distribution function within a quantum Boltzmann equation approach. We find that the thermalization rates are proportional to the square of the next-to-nearest neighbor hopping: Even weak next-to-nearest neighbor hopping in addition to nearest neighbor hopping leads to thermalization in a two-particle scattering quantum Boltzmann equation in one dimension. We also investigate the temperature dependence of the thermalization rates, which away from half filling become exponentially small for small temperature of the final thermalized distribution.