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arXiv:0912.0373 · Physical Review C

Quantum Monte Carlo study of dilute neutron matter at finite temperatures

Gabriel Wlazłowski, Piotr Magierski

Published Jan 31, 2011• 13 citations
arXivHTMLPDF

Abstract

We report results of fully nonperturbative, path integral Monte Carlo calculations for dilute neutron matter. The neutron-neutron interaction in the $s$ channel is parameterized by the scattering length and the effective range. We calculate the energy and the chemical potential as a function of temperature at density $\ensuremath{\rho}=0.003 {\text{fm}}^{\ensuremath{-}3}$. The critical temperature ${T}_{c}$ for the superfluid-normal phase transition is estimated from the finite size scaling of the condensate fraction. At low temperatures we extract the spectral weight function $A(\mathbf{p},\ensuremath{\omega})$ from the imaginary time propagator using the methods of maximum entropy and singular value decomposition. We determine the quasiparticle spectrum, which can be accurately parameterized by three parameters: an effective mass ${m}^{*}$, a mean-field potential $U$, and a gap $\ensuremath{\Delta}$. Large values of $\ensuremath{\Delta}/{T}_{c}$ indicate that the system is not a BCS-type superfluid at low temperatures.

DOI
10.1103/physrevc.83.012801

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The quantum Monte Carlo method for spin-12\frac{1}{2}21​ fermions at finite temperature is formulated for dilute systems with an sss-wave interaction. The motivation and the formalism are discussed along with descriptions of the algorithm and various numerical issues. We report on results for the energy, entropy, and chemical potential as a function of temperature. We give upper bounds on the critical temperature Tc{T}_{c}Tc​ for the onset of superfluidity, obtained by studying the finite-size scaling of the condensate fraction. All of these quantities were computed for couplings around the unitary regime in the range $\ensuremath{-}0.5\ensuremath{\leqslant}{({k}_{F}a)}^{\ensuremath{-}1}\ensuremath{\leqslant}0.2$, where aaa is the sss-wave scattering length and kF{k}_{F}kF​ is the Fermi momentum of a noninteracting gas at the same density. In all cases our data are consistent with normal Fermi gas behavior above a characteristic temperature T0>Tc{T}_{0}>{T}_{c}T0​>Tc​, which depends on the coupling and is obtained by studying the deviation of the caloric curve from that of a free Fermi gas. For Tc<T<T0{T}_{c}<T<{T}_{0}Tc​<T<T0​ we find deviations from normal Fermi gas behavior that can be attributed to pairing effects. Low-temperature results for the energy and the pairing gap are shown and compared with Green-function Monte Carlo results by other groups.
Thermal properties of low-density neutron matter are investigated by determinantal quantum Monte Carlo lattice calculations on 3+1 dimensional cubic lattices. Nuclear effective field theory (EFT) is applied using the pionless single- and two-parameter neutron-neutron interactions, determined from the 1S0{}^{1}{S}_{0}1S0​ scattering length and effective range. The determination of the interactions and the calculations of neutron matter are carried out consistently by applying EFT power counting rules. The thermodynamic limit is taken by the method of finite-size scaling, and the continuum limit is examined in the vanishing lattice filling limit. The 1S0{}^{1}{S}_{0}1S0​ pairing gap at $T\ensuremath{\approx}0$ is computed directly from the off-diagonal long-range order of the spin pair-pair correlation function and is found to be approximately 30% smaller than BCS calculations with the conventional nucleon-nucleon potentials. The critical temperature Tc{T}_{c}Tc​ of the normal-to-superfluid phase transition and the pairing temperature scale T∗{T}^{*}T∗ are determined, and the temperature-density phase diagram is constructed. The physics of low-density neutron matter is clearly identified as being a BCS-Bose-Einstein condensation crossover.
By using exact path-integral Monte Carlo methods we calculate the equation of state of an interacting Bose gas as a function of temperature both below and above the superfluid transition. The universal character of the equation of state for dilute systems and low temperatures is investigated by modeling the interatomic interactions using different repulsive potentials corresponding to the same sss-wave scattering length. The results obtained for the energy and the pressure are compared to the virial expansion for temperatures larger than the critical temperature. At very low temperatures we find agreement with the ground-state energy calculated using the diffusion Monte Carlo method.
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Various quantities of an attractively interacting fermion system at the unitary limit are determined by extrapolating Monte Carlo results of low-density neutron matter. Smooth extrapolation in terms of 1/(kFa0)1/({k}_{F}{a}_{0})1/(kF​a0​) (kF{k}_{F}kF​ is the Fermi momentum, and a0{a}_{0}a0​ is the 1S0{}^{1}{S}_{0}1S0​ scattering length) is found with the quantities examined: the ground-state energy, the pairing gap at $T\ensuremath{\approx}0$, and the critical temperature of the normal-to-superfluid phase transition. We emphasize proximity of the physics of low-density neutron matter to that at the unitary limit. The extrapolated quantities are in a reasonable agreement with those in the literature.