Cold dilute neutron matter on the lattice. I. Lattice virial coefficients and large scattering lengths

We study cold dilute neutron matter on the lattice using an effective field theory. We work in the unitary limit in which the scattering length is much larger than the interparticle spacing. In this article we focus on the equation of state at temperatures above the Fermi temperature and compare lattice simulations to the virial expansion on the lattice and in the continuum. We find that in the unitary limit lattice discretization errors in the second virial coefficient are significantly enhanced. As a consequence the equation of state does not show the universal scaling behavior expected in the unitary limit. We suggest that scaling can be improved by tuning the second virial coefficient rather than the scattering length.

Figure 1

Diagrams contributing to neutron-neutron scattering.

Figure 2

Energy per neutron versus density at $T=4$ MeV for various scattering lengths.

Figure 3

Energy per neutron versus density at $T=3$ MeV for various scattering lengths.

Figure 4

Energy per neutron versus density at $T=2$ MeV for various scattering lengths.

Figure 5

Bubble chain diagrams contributing to the neutron self-energy.

Figure 6

Bubble chain diagrams contributing to the logarithm of the partition function.

Figure 7

Density versus fugacity at $T=4$ MeV for scattering lengths $a_{\mathrm{scatt}}=\pm 18.70$ fm. We show comparisons with the first- and second-order virial expansion.

Figure 8

Density versus fugacity at $T=3$ MeV for scattering lengths $a_{\mathrm{scatt}}=\pm 18.70$ fm. We show comparisons with the first- and second-order virial expansion.

Figure 9

Density versus fugacity at $T=2$ MeV for scattering lengths $a_{\mathrm{scatt}}=\pm 18.70$ fm. We show comparisons with the first- and second-order virial expansion.

Figure 10

Plot of second virial coefficient as function of inverse scattering length for various temperatures. The smooth curves are the continuum results, and the points with interpolating lines are the lattice results.

Figure 11

Plot of continuum and lattice virial results for $T=1$ MeV. We also show the lattice results shifted horizontally so that $b_2$ equals $0.530$ at infinite scattering length.

Figure 12

Plot of continuum and lattice virial results for $T=0.5$ MeV. We also show the lattice results shifted horizontally so that $b_2$ equals $0.530$ at infinite scattering length.