Critical behavior driven by the confining potential in optical lattices with ultra-cold fermions?

TL;DR

This paper explores how the ground-state energy of ultra-cold fermions in optical lattices exhibits critical behavior influenced by the confining potential, using a two-parameter scaling approach and density functional theory.

Contribution

It provides a detailed analysis of critical phenomena in fermionic Hubbard models under confining potentials, extending previous scaling methods to include the effects of trap shape.

Findings

Signatures of critical behavior as the potential exponent alpha approaches infinity.

Validation of the two-parameter scaling method for phase diagram determination.

Application of BALDA-DFT to analyze ground-state energy dependence on trap parameters.

Abstract

A recent paper [V. L. Campo et. al., Phys. Rev. Lett. 99, 240403 (2007) has proposed a two-parameter scaling method to determine the phase diagram of the fermionic Hubbard model from optical lattice experiments. Motivated by this proposal, we investigate in more detail, the behavior of the ground-state energy per site as a function of trap size(L) and confining potential (V(x) = t(x/L)^alpha) in the one-dimensional case. Using the BALDA-DFT method, we find signatures of critical behavior as alpha goes to infinity.