Article

# Quantum Monte Carlo Method Applied to Strongly Correlated Dilute Fermi Gases with Finite Effective Range

(Impact Factor: 1.34). 04/2009; 18(04):919-925. DOI: 10.1142/S0218301309013051
Source: arXiv

ABSTRACT

We discuss the Auxiliary Field Quantum Monte Carlo (AFQMC) method
applied to dilute neutron matter at finite temperatures. We formulate
the discrete Hubbard-Stratonovich transformation for the interaction
with finite effective range which is free from the sign problem. The
AFQMC results are compared with those obtained from exact
diagonalization for a toy model. Preliminary calculations of energy and
chemical potential as a function of temperature are presented.

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ABSTRACT: The relation between the interaction parameters for fermions on the spatial lattice and the two-body $T$ matrix is discussed. The presented method allows determination of the interaction parameters through the relatively simple computational scheme which include the effect of finite lattice spacing. In particular the relation between the interaction parameters and the effective range expansion parameters is derived in the limit of large lattices. Comment: Proceedings from XVI Nuclear Physics Workshop in Kazimierz Dolny, Poland. Accepted to publish in the International Journal of Modern Physics E, vol. 19
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##### Article: The Unitary Fermi Gas: From Monte Carlo to Density Functionals
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ABSTRACT: In this chapter, we describe three related studies of the universal physics of two-component unitary Fermi gases with resonant short-ranged interactions. First we discuss an ab initio auxiliary field quantum Monte Carlo technique for calculating thermodynamic properties of the unitary gas from first principles. We then describe in detail a Density Functional Theory (DFT) fit to these thermodynamic properties: the Superfluid Local Density Approximation (SLDA) and its Asymmetric (ASLDA) generalization. We present several applications, including vortex structure, trapped systems, and a supersolid Larkin-Ovchinnikov (FFLO/LOFF) state. Finally, we discuss the time-dependent extension to the density functional (TDDFT) which can describe quantum dynamics in these systems, including non-adiabatic evolution, superfluid to normal transitions and other modes not accessible in traditional frameworks such as a Landau-Ginzburg, Gross-Pitaevskii, or quantum hydrodynamics.
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