Quantum Monte Carlo study of confined fermions in one-dimensional optical lattices

TL;DR

This study uses quantum Monte Carlo simulations to analyze the ground-state properties of confined one-dimensional fermionic systems in optical lattices, revealing local behaviors and phase diagrams relevant for experiments.

Contribution

It introduces a local compressibility measure for identifying Mott-insulating regions and compares QMC results with mean-field approaches for these systems.

Findings

Local compressibility effectively characterizes Mott-insulating regions.

Momentum distribution fails to clearly signal the Mott transition.

A generic phase diagram predicts experimental phases.

Abstract

Using quantum Monte Carlo (QMC) simulations we study the ground-state properties of the one-dimensional fermionic Hubbard model in traps with an underlying lattice. Since due to the confining potential the density is space dependent, Mott-insulating domains always coexist with metallic regions, such that global quantities are not appropriate to describe the system. We define a local compressibility that characterizes the Mott-insulating regions and analyze other local quantities. It is shown that the momentum distribution function, a quantity that is commonly considered in experiments, fails in giving a clear signal of the Mott-insulator transition. Furthermore, we analyze a mean-field approach to these systems and compare it with the numerically exact QMC results. Finally, we determine a generic form for the phase diagram that allows us to predict the phases to be observed in the experiments.