Dispersive spectrum and orbital order of spinless p-band fermions in an optical lattice

TL;DR

This paper investigates the spectral properties and orbital ordering of spinless p-band fermions in an optical lattice, revealing flat spectra at half-filling, orbital order transitions with doping, and potential ferromagnetic order at low fillings.

Contribution

It introduces a variational cluster approach to analyze orbital orderings and spectral functions, and proposes a new method for efficient Matsubara-frequency summation.

Findings

Spectral function is flat at half-filling and dispersive at lower fillings.

Antiferromagnetic orbital order at half-filling is disrupted by doping.

Potential ferromagnetic orbital order at low fillings.

Abstract

We study single-particle properties of a spinless p-band correlated fermionic gas in an optical lattice by means of a variational cluster approach (VCA). The single-particle spectral function is almost flat at half-filling and develops a strongly dispersive behavior at lower fillings. The competition between different orbital orderings is studied as a function of filling. We observe that an ``antiferromagnetic'' orbital order develops at half-filling and is destroyed by doping the system evolving into a disordered orbital state. At low filling limit, we discuss the possibility of ``ferromagnetic'' orbital order by complementing the VCA result with observations based on a trial wave function. We also study the behavior of the momentum distribution for different values of the on-site interaction. Finally, we introduce an integration contour in the complex plane which allows to efficiently carry out Matsubara-frequency sums.