We simulate the dilute attractive Fermi-Hubbard model in the unitarity regime using a diagrammatic determinant Monte Carlo algorithm with worm-type updates. We obtain the dependence of the critical temperature on the filling factor
ν and, by extrapolating to
ν→0, determine the universal critical temperature of the continuum unitary Fermi gas in units of Fermi energy:
Tc/εF=0.152(7). We also determine the thermodynamic functions and show how the Monte Carlo results can be used for accurate thermometry of a trapped unitary gas.
In this article we present a Monte Carlo calculation of the critical temperature and other thermodynamic quantities for the unitary Fermi gas with a population imbalance (unequal number of fermions in the two spin components). We describe an improved worm-type algorithm that is less prone to autocorrelations than the previously available methods and show how this algorithm can be applied to simulate the unitary Fermi gas in presence of a small imbalance. Our data indicate that the critical temperature remains almost constant for small imbalances $h=\ensuremath{\Delta}\ensuremath{\mu}/{\ensuremath{\varepsilon}}_{F}\ensuremath{\lesssim}0.2$. We obtain the continuum result ${T}_{c}=0.171(5){\ensuremath{\varepsilon}}_{F}$ in units of Fermi energy and derive a lower bound on the deviation of the critical temperature from the balanced limit, ${T}_{c}(h)\ensuremath{-}{T}_{c}(0)>\ensuremath{-}0.5{\ensuremath{\varepsilon}}_{F}{h}^{2}$. Using an additional assumption a tighter lower bound can be obtained. We also calculate the energy per particle and the chemical potential in the balanced and imbalanced cases.
We study the thermodynamics of the three-dimensional Hubbard model at half filling on approach to the N\'eel transition by means of large-scale unbiased diagrammatic determinant Monte Carlo simulations. We obtain the transition temperature in the strongly correlated regime, as well as the temperature dependence of the energy, entropy, double occupancy, and nearest-neighbor spin correlation function. Our results improve the accuracy of previous unbiased studies and present accurate benchmarks in the ongoing effort to realize the antiferromagnetic state of matter with ultracold atoms in optical lattices.
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.