We calculate the one-body temperature Green's (Matsubara) function of the unitary Fermi gas via quantum Monte Carlo, and extract the spectral weight function A(p,omega) using the methods of maximum entropy and singular value decomposition. From A(p,omega) we determine the quasiparticle spectrum, which can be accurately parametrized by three functions of temperature: an effective mass m{*}, a mean-field potential U, and a gap Delta. Below the critical temperature T{c}=0.15 epsilon{F} the results for m{*}, U, and Delta can be accurately reproduced using an independent quasiparticle model. We find evidence of a pseudogap in the fermionic excitation spectrum for temperatures up to T{*} approximately 0.20 epsilon{F}> T{c}.
We calculate the one-body temperature Green's (Matsubara) function of the unitary Fermi gas via quantum Monte Carlo, and extract the spectral weight function A(p,omega) using the methods of maximum entropy and singular value decomposition. From A(p,omega) we determine the quasiparticle spectrum, which can be accurately parametrized by three functions of temperature: an effective mass m{}, a mean-field potential U, and a gap Delta. Below the critical temperature T{c}=0.15 epsilon{F} the results for m{}, U, and Delta can be accurately reproduced using an independent quasiparticle model. We find evidence of a pseudogap in the fermionic excitation spectrum for temperatures up to T{*} approximately 0.20 epsilon{F}> T{c}.
The unitary Fermi gas (UFG) is a strongly correlated system of two-species (spin-1/2) fermions with a short-range attractive interaction modeled by a contact interaction and has attracted much interest across different disciplines. The UFG is considered a paradigm for strongly correlated superfluids and has been investigated extensively, with generally good agreement found between theory and experiment. However, the extent of a pseudogap regime above the critical temperature Tc for superfluidity is still debated both theoretically and experimentally. Here we study thermodynamic properties of the UFG across the superfluid phase transition using finite-temperature lattice auxiliary-field quantum Monte Carlo (AFMC) methods in the canonical ensemble of fixed particle numbers. We extrapolate our lattice AFMC results to the continuous time and continuum limits, thus removing the systematic error associated with the finite filling factor of previous AFMC studies. We determine the critical temperature to be Tc=0.16(1)TF. For the largest particle number studied N=114, the energy-staggering pairing gap is suppressed above a pairing scale temperature of T∗≈0.2TF. The spin susceptibility displays moderate suppression above Tc with a spin gap temperature of Ts≈0.2TF. We also calculate a free energy-staggering pairing gap, which shows substantially reduced statistical errors when compared with the energy-staggering gap, allowing for a clear signature of pairing correlations in the finite-size system. All results indicate that the pseudogap regime is narrow, with pseudogap signatures emerging at temperatures below T∗≈0.2TF. The reduced statistical errors of the free energy gap enable an extrapolation at low temperatures, allowing an estimate of the zero-temperature pairing gap ΔE=0.576(24)εF.
In the two-component Fermi gas with a contact interaction, a pseudogap regime can exist at temperatures between the superfluid critical temperature T_{c} and a temperature T^{*}>T_{c}. This regime is characterized by pairing correlations without superfluidity. However, in the unitary limit of infinite scattering length, the existence of this regime is still debated. To help address this, we have applied finite-temperature auxiliary-field quantum Monte Carlo (AFMC) methods to study the thermodynamics of the superfluid phase transition and signatures of the pseudogap in the spin-balanced homogeneous unitary Fermi gas. We present results at finite filling factor ν≃0.06 for the condensate fraction, an energy-staggering pairing gap, the spin susceptibility, and the heat capacity, and compare them to experimental data when available. In contrast to previous AFMC simulations, our model space consists of the complete first Brillouin zone of the lattice, and our calculations are performed in the canonical ensemble of fixed particle number. The canonical ensemble AFMC framework enables the calculation of a model-independent gap, providing direct information on pairing correlations without the need for numerical analytic continuation. We use finite-size scaling to estimate T_{c} at the corresponding filling factor. We find that the energy-staggering pairing gap vanishes above T_{c}, showing no pseudogap effects, and that the spin susceptibility shows a substantially reduced signature of a spin gap compared to previously reported AFMC simulations.
The radio-frequency spectrum of the fermions in the unitary limit at finite temperatures is characterized by the sum-rule relations. We consider a simple picture where the atoms are removed by radio-frequency excitations from the strongly interacting states into a state of negligible interaction. We calculate the moments of the response function in the range of temperature 0.08ϵF<T<0.8ϵF using auxiliary field Monte Carlo technique in which continuum auxiliary fields with a density-dependent shift are used. We estimate the effects of superfluid pairing from the clock shift. We find a qualitative agreement with the pairing gap--pseudogap transition behavior. We also find within the quasiparticle picture that in order for the gap to come into quantitative agreement with the previously known value at T=0, the effective mass has to be ${m}^{\ensuremath{\ast}}\ensuremath{\sim}1.43m$. Finally, we discuss implications for the adiabatic sweep of the resonant magnetic field.
In the two-component Fermi gas with contact interactions a pseudogap regime, in which pairing correlations are present without superfluidity, can exist at temperatures between the superfluid critical temperature Tc and a temperature T∗>Tc. However, the existence of a pseudogap in the unitary limit of infinite scattering length is debated. To help address this issue, we have used finite-temperature auxiliary-field quantum Monte Carlo (AFMC) methods to study the thermodynamics of the spin-balanced homogeneous unitary Fermi gas on a lattice. We present results for the thermal energy, heat capacity, condensate fraction, a model-independent pairing gap, and spin susceptibility, and compare them to experimental data when available. Our model space consists of the complete first Brillouin zone of the lattice, and our calculations are performed in the canonical ensemble of fixed particle number. We find that the energy-staggering pairing gap vanishes above Tc and that T∗ at unitarity, as determined from the spin susceptibility, is lower than previously reported in AFMC simulations.
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 Tc 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.
The quantum Monte Carlo method for spin-21 fermions at finite temperature is formulated for dilute systems with an s-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 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 a is the s-wave scattering length and 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, 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 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.