Abstract
In recent years Quantum Monte Carlo techniques provided to be a valuable tool to study strongly interacting Fermi gases at zero temperature. We have used QMC methods to investigate several properties of the two-components Fermi gas at unitarity and in the BCS-BEC crossover, both with equal and unequal masses corresponding to the Li – K Fermi mixture. In this paper we present several recent QMC results, including the energy at zero and finite effective range, the contact parameter and the static structure factor, which, at low momentum, depends strongly on the phonons in the unitary Fermi gas.
Highlights
During the last years important efforts have been devoted to study ultra-cold Fermi gases, both experimentally and theoretically
These systems can be experimentally studied at very low temperatures of the order of 0.1 TF, essentially zero temperature. They are very dilute, and their properties are independent of the form of the Hamiltonian used to describe the system, the results given by any model satisfying the limits of large scattering length and small effective range must be identical
The Auxiliary Field Monte Carlo (AFMC) performed on a lattice through the use of auxiliary fields does not suffer of the Fermion sign problem and permits to calculate exactly the energy of the unpolarized Fermi gas [21]
Summary
During the last years important efforts have been devoted to study ultra-cold Fermi gases, both experimentally and theoretically (for a review see for example Ref. [1]). The study of ultra-cold Fermi gases is very intriguing, and the unitary limit became a very interesting many-body problem to solve for several reasons These systems can be experimentally studied at very low temperatures of the order of 0.1 TF , essentially zero temperature. They are very dilute, and their properties are independent of the form of the Hamiltonian used to describe the system, the results given by any model satisfying the limits of large scattering length and small effective range must be identical. In this paper we will review several properties calculated using QMC methods, including the exact calculation of the energy, the role of the effective range, the BCS-BEC crossover, and other properties including the contact parameter and the static structure factor
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