2 research outputs found
Generalized Hartree-Fock Theory for Interacting Fermions in Lattices: Numerical Methods
We present numerical methods to solve the Generalized Hartree-Fock theory for
fermionic systems in lattices, both in thermal equilibrium and out of
equilibrium. Specifically, we show how to determine the covariance matrix
corresponding to the Fermionic Gaussian state that optimally approximates the
quantum state of the fermions. The methods apply to relatively large systems,
since their complexity only scales quadratically with the number of lattice
sites. Moreover, they are specially suited to describe inhomogenous systems, as
those typically found in recent experiments with atoms in optical lattices, at
least in the weak interaction regime. As a benchmark, we have applied them to
the two-dimensional Hubbard model on a 10x10 lattice with and without an
external confinement.Comment: 16 pages, 22 figure
A real space auxiliary field approach to the BCS-BEC crossover
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
scale that agrees with quantum Monte Carlo estimates to within a few
percent. We provide results on the , 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.Comment: This article supersedes arXiv:1105.115