arXiv:0812.0883v1 [nucl-th] 4 Dec 2008
International Journal of Modern Physics E
c ? World Scientific Publishing Company
QUANTUM MONTE CARLO METHOD APPLIED TO STRONGLY
CORRELATED DILUTE FERMI GASES WITH FINITE
GABRIEL WLAZ? LOWSKI and PIOTR MAGIERSKI
Faculty of Physics, Warsaw University of Technology, ul. Koszykowa 75
00-662 Warsaw, Poland
e-mail: email@example.com, firstname.lastname@example.org
Received (received date)
Revised (revised date)
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.
Properties of dilute and degenerate Fermi gases with large scattering lengths are of
particular interest in the context of cold fermionic atoms and dilute neutron matter.
In the case of trapped fermionic atoms, due to very low density, the scattering
length is the only parameter which determines an atom-atom interaction. Taking
advantage of Feshbach resonances it can be tuned, using external magnetic field,
to the values which greatly exceed the average interparticle distance. This limit
which is dubbed the unitary regime exhibits universal properties and has been the
subject of intensive theoretical effort in the last couple of years (see1and references
therein). Similarly, neutron matter at densities corresponding to kF ? 0.6 fm−1is
a dilute system of fermions in a sense that the average distance between particles
is much larger than the range of the neutron-neutron interaction. It is superfluid
and its physics is determined by two parameters: scattering length aSand effective
range reffin1S0neutron-neutron channel. The influence of other channels as well
as of three-body forces is marginal and can be neglected in this density range2.
The properties of dilute neutron matter are crucial for understanding the structure
and thermal evolution of neutron star crust3. They can also provide constraints for
parameters of nuclear energy density functional.
Despite of these similarities the important qualitative difference between dilute
neutron matter and cold atomic gases arises from the fact that in the former case
Quantum Monte-Carlo study of strongly correlated dilute fermionic gases
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