Time evolution of the local density of states of strongly correlated fermions coupled to a nanoprobe

TL;DR

This paper investigates how strong electron interactions affect the time-dependent local density of states in a one-dimensional Hubbard model system after coupling to a nanoprobe, revealing nontrivial dynamics and Mott gap melting.

Contribution

It introduces a detailed study of the non-equilibrium dynamics of strongly correlated electrons using time-dependent matrix product states, focusing on local LDOS evolution after a local perturbation.

Findings

Interactions induce nontrivial LDOS dynamics absent in noninteracting systems

The Mott gap locally closes and propagates through the system over time

Particle oscillations between the sample and nanoprobe are characterized

Abstract

We study the time evolution of a one-dimensional system of strongly correlated electrons (a 'sample') that is suddenly coupled to a smaller, initially empty system (a 'nanoprobe'), which can subsequently move along the system. Our purpose here is to study the role of interactions in this model system when it is far from equilibrium. We therefore take both the sample and the nanoprobe to be described by a Hubbard model with on-site repulsive interactions and nearest-neighbor hopping. We compute the behavior of the local particle density and the local density of states (LDOS) as a function of time using time-dependent matrix product states at quarter and at half filling, fillings at which the chain realizes a Luttinger liquid or a Mott insulator, respectively. This allows us to study in detail the oscillation of the particles between the sample and the nanoprobe. While, for noninteracting systems, the LDOS is time-independent, in the presence of interactions, the backflow of electrons to the sample will lead to nontrivial dynamics in the LDOS. In particular, studying the time-dependent LDOS allows us to study how the Mott gap closes locally and how this melting of the Mott insulator propagates through the system in time after such a local perturbation -- a behavior that we envisage can be investigated in future experiments on ultrashort time scales or on optical lattices using microscopy setups.