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 ${}^{1}{S}_{0}$ 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 ${}^{1}{S}_{0}$ 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 ${T}_{c}$ of the normal-to-superfluid phase transition and the pairing temperature scale ${T}^{*}$ 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.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 ${}^{1}{S}_{0}$ 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 ${}^{1}{S}_{0}$ 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 ${T}_{c}$ of the normal-to-superfluid phase transition and the pairing temperature scale ${T}^{*}$ 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.

arXiv:0708.2523Physical Review CMay 11, 200945 citations

Pairing in Non-Fermi Liquids in Terms of Bethe-Salpeter Equation

YURIY M. MALOZOVSKY, Jingtao Fan

Bulletin of the American Physical SocietyMar 12, 20080 citations

From low-density neutron matter to the unitary limit

Takumi Abe, R. Seki

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 $1/({k}_{F}{a}_{0})$ ( ${k}_{F}$ is the Fermi momentum, and ${a}_{0}$ is the ${}^{1}{S}_{0}$ 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.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 $1/({k}_{F}{a}_{0})$ (${k}_{F}$ is the Fermi momentum, and ${a}_{0}$ is the ${}^{1}{S}_{0}$ 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.

arXiv:0708.2524Physical Review CMay 11, 200937 citations

^1S_0

1 S 0 Pairing in Neutron Matter

{}^{1}{S}_{0}

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

{}^{1}{S}_{0}

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

{T}_{c}

of the normal-to-superfluid phase transition and the pairing temperature scale

{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.

1/({k}_{F}{a}_{0})

(

{k}_{F}

is the Fermi momentum, and

{a}_{0}

is the

{}^{1}{S}_{0}

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.