Local quantum criticality in confined fermions on optical lattices

TL;DR

This paper demonstrates that confined fermions in optical lattices exhibit local quantum criticality at Mott-insulating boundaries, with universal behavior and critical exponents, using quantum Monte Carlo simulations.

Contribution

It reveals the critical behavior and universality of local compressibility in the one-dimensional fermionic Hubbard model under harmonic confinement.

Findings

Identification of quantum critical behavior at Mott-insulating boundaries

Universality of local compressibility and density variance

A phase diagram predicting experimental phases in ultracold fermionic atoms

Abstract

Using quantum Monte Carlo simulations, we show that the one-dimensional fermionic Hubbard model in a harmonic potential displays quantum critical behavior at the boundaries of a Mott-insulating region. A local compressibility defined to characterize the Mott-insulating phase has a non-trivial critical exponent. Both the local compressibility and the variance of the local density show universality with respect to the confining potential. We determine a generic phase diagram, that allows the prediction of the phases to be observed in experiments with ultracold fermionic atoms trapped on optical lattices.