Eur. Phys. J. B (2015) 88: 68
https://doi.org/10.1140/epjb/e2015-50284-6

Regular Article

A real space auxiliary field approach to the BCS-BEC crossover

Harish-Chandra Research Institute, Chhatnag Road, Jhusi, 211019 Allahabad, India

^a e-mail: terubrahms@gmail.com

Received: 5 May 2014
Received in final form: 6 October 2014
Published online: 19 March 2015

Abstract

The BCS to BEC crossover in attractive Fermi systems is a prototype of weak to strong coupling evolution in many body physics. While extensive numerical results are available, and several approximate methods have been developed, most of these schemes are unsuccessful in the presence of spatial inhomogeneity. Such situations call for a real space approach that can handle large spatial scales and retain the crucial thermal fluctuations. With this in mind we present comprehensive results of a real space auxiliary field approach to the BCS to BEC crossover in the attractive Hubbard model in two dimensions. The scheme reproduces the Hartree-Fock-Bogoliubov ground state, and leads to a T_c scale that agrees with quantum Monte Carlo estimates to within a few percent. We provide results on the T_c, amplitude and phase fluctuations, density of states, and the momentum resolved spectral function, over the entire interaction and temperature window. We suggest how the method generalises successfully to the presence of disorder, trapping, and population imbalance.