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arXiv · 1304.1645

Configuration-interaction Monte Carlo method and its application to the trapped unitary Fermi gas

Abhishek Mukherjee·Y. Alhassid
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Abstract

We develop a quantum Monte Carlo method to estimate the ground-state energy of a fermionic many-particle system in the configuration-interaction shell model approach. The fermionic sign problem is circumvented by using a guiding wave function in Fock space. The method provides an upper bound on the ground-state energy whose tightness depends on the choice of the guiding wave function. We argue that the antisymmetric geminal product class of wave functions is a good choice for guiding wave functions. We demonstrate our method for the trapped two-species fermionic cold atom system in the unitary regime of infinite scattering length using the particle-number projected Hartree-Fock-Bogoliubov wave function as the guiding wave function. We estimate the ground-state energy and energy-staggering pairing gap as a function of the number of particles. Our results compare favorably with exact numerical diagonalization results and with previous coordinate-space Monte Carlo calculations.

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Abhishek Mukherjee, Y. Alhassid. 2013-04-05. Configuration-interaction Monte Carlo method and its application to the trapped unitary Fermi gas. https://doi.org/10.1103/physreva.88.053622

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