Ultracold atoms at unitarity within quantum Monte Carlo methods

Andrew J. Morris, P. López Ríos, and R. J. Needs
Phys. Rev. A 81, 033619 – Published 23 March 2010

Abstract

Variational and diffusion quantum Monte Carlo (VMC and DMC) calculations of the properties of the zero-temperature fermionic gas at unitarity are reported. Our study differs from earlier ones mainly in that we have constructed more accurate trial wave functions and used a larger system size, we have studied the dependence of the energy on the particle density and well width, and we have achieved much smaller statistical error bars. The correct value of the universal ratio of the energy of the interacting to that of the noninteracting gas, ξ, is still a matter of debate. We find DMC values of ξ of 0.4244(1) with 66 particles and 0.4339(1) with 128 particles. The spherically averaged pair-correlation functions, momentum densities, and one-body density matrices are very similar in VMC and DMC, which suggests that our results for these quantities are very accurate. We find, however, some differences between the VMC and DMC results for the two-body density matrices and condensate fractions, which indicates that these quantities are more sensitive to the quality of the trial wave function. Our best estimate of the condensate fraction of 0.51 is smaller than the values from earlier quantum Monte Carlo calculations.

    • Received 2 October 2009

    DOI:https://doi.org/10.1103/PhysRevA.81.033619

    ©2010 American Physical Society

    Authors & Affiliations

    Andrew J. Morris*, P. López Ríos, and R. J. Needs

    • Theory of Condensed Matter Group, Cavendish Laboratory, University of Cambridge, J.J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom

    • *andrew.morris@ucl.ac.uk; Current address: Dept. Physics and Astronomy, University College London, Gower Street, London, WC1 6BT, United Kingdom.

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    Issue

    Vol. 81, Iss. 3 — March 2010

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