Cold dilute neutron matter on the lattice. II. Results in the unitary limit

This is the second of two articles that investigate cold dilute neutron matter on the lattice using pionless effective field theory. In the unitary limit, where the effective range is zero and scattering length is infinite, simple scaling relations relate thermodynamic functions at different temperatures. When the second virial coefficient is properly tuned, we find that the lattice results obey these scaling relations. We compute the energy per particle, pressure, spin susceptibility, dineutron correlation function, and an upper bound for the superfluid critical temperature.

Figure 1

Density times ${\lambda }_T^3$ versus fugacity for various temperatures.

Figure 2

Density times ${\lambda }_T^3$ versus fugacity for small fugacity. We also include comparisons with the virial expansion at first and second orders.

Figure 3

Energy per particle times β versus fugacity. We show results for $T=4,3,$ $2,$ $1.5,$ and 1 MeV.

Figure 4

Energy per particle times β versus fugacity at small fugacity. We compare with first- and second-order virial expansion results.

Figure 5

Energy density times $\beta {\lambda }_T^3$ versus fugacity for various temperatures. We compare with the pressure times $\frac{3}{2}\beta {\lambda }_T^3.$

Figure 6

The energy per particle divided by $\frac{3}{5}{E}_F$ versus temperature divided by $T_F$ for temperatures $T=4,3,$ $2,$ $1.5,$ and 1 MeV.

Figure 7

A magnified plot at low temperatures of the energy per particle divided by $\frac{3}{5}{E}_F$ versus temperature divided by $T_F$.

Figure 8

Lattice results for the axial response as a function of fugacity for temperatures $T=4,3,$ $2,$ $1.5,$ and 1 MeV.

Figure 9

Logarithm of the dineutron correlation function versus lattice distance measured along a lattice axis. We show results for $T=1$ MeV$.$