On the nonlinear response of a particle interacting with fermions in a 1D lattice

TL;DR

This paper investigates the nonlinear energy response of a particle interacting with fermions in a 1D lattice, revealing how collective effects and Fermi properties influence Bloch oscillations and temperature independence.

Contribution

It provides an analytical study of the particle-fermion interaction using Bethe ansatz, highlighting the collective origin of dispersion and temperature effects in 1D systems.

Findings

Dispersion related to Fermi wavevector and collective effects

Temperature independence at half-filling

Adiabatic response to applied fields

Abstract

By the Bethe ansatz method we study the energy dispersion of a particle interacting by a local interaction with fermions (or hard core bosons) of equal mass in a one dimensional lattice. We focus on the period of the Bloch oscillations which turns out to be related to the Fermi wavevector of the Fermi sea and in particular on how this dispersion emerges as a collective effect in the thermodynamic limit. We show by symmetry that the dispersion is temperature independent for a half-filled system. We also discuss the adiabatic coherent collective response of the particle to an applied field.