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arXiv:cond-mat/0605350

The Fermi-Hubbard model at unitarity

Evgeni Burovski, Nikolay V. Prokof'ev, Boris V. Svistunov, Matthias Troyer

Published May 12, 2006• 6 citations
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Abstract

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 $ν\to 0$, determine the universal critical temperature of the continuum unitary Fermi gas in units of Fermi energy: $T_c/ε_F=0.152(7)$. We also determine the thermodynamic functions and show how the Monte Carlo results can be used for accurate thermometry of a trapped unitary gas.

DOI
10.48550/arxiv.cond-mat/0605350

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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 ννν and, by extrapolating to ν→0ν\to 0ν→0, determine the universal critical temperature of the continuum unitary Fermi gas in units of Fermi energy: Tc/εF=0.152(7)T_c/ε_F=0.152(7)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.
We simulate the dilute attractive Fermi–Hubbard model in the unitarity regime using a diagrammatic determinant Monte Carlo (MC) 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: T c /ε F = 0.152(7). We also determine the thermodynamic functions and show how the MC 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.
A recent paper by T. Papenbrock [Phys. Rev. A 72, 041602(R) (2005)] suggests that a determination of the universal factor ${\ensuremath{\xi}}_{3\mathrm{D}}$ for a harmonically trapped, unpolarized dilute Fermi gas in the unitary regime may be obtained within the framework of a simple density-functional theory (DFT). One of the key results of that work is an estimate for the universal factor ${\ensuremath{\xi}}_{3\mathrm{D}}\ensuremath{\approx}0.54$, which is within 20% of the generally accepted quantum Monte Carlo simulation value of ${\ensuremath{\xi}}_{3\mathrm{D}}=0.44\ifmmode\pm\else\textpm\fi{}0.01$. Motivated by this result, this report investigates the determination of the universal factor ${\ensuremath{\xi}}_{2\mathrm{D}}$ for a two-dimensional trapped Fermi gas, and suggests that the simple DFT approach of Papenbrock provides an exact result of ${\ensuremath{\xi}}_{2\mathrm{D}}=1$ in two dimensions.
A generic scenario of a crossover between weak-coupling and strong-coupling limits of a many-body quantum system is studied. Powerful numerical methods of investigating the strongly correlated regime are developed and applied to answering a number of important questions of the strongly correlated fermions physics. The internal structure of an exciton in an insulating medium is studied throughout the crossover between the (analytically solvable) strong- and weak-coupling limits. In the intermediate regime, accurate results for the exciton ground state are obtained and used to establish the limits of applicability of the corresponding limiting cases for the first time. A novel combination of the diagrammatic determinant Monte Carlo and the worm algorithm is developed and used for investigating the unitarity regime of the BEC-BCS crossover via simulating the dilute Fermi-Hubbard model. Superfluid phase transition and thermodynamic properties of the normal state are characterized for both lattice fermions and continuum unitary Fermi gas. The relation to current experiments with trapped ultracold quantum gases is discussed.