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arXiv:1102.1318 · Physical Review B

Quantum Monte Carlo calculation of the zero-temperature phase diagram of the two-component fermionic hard-core gas in two dimensions

N. D. Drummond, Nigel R. Cooper, Richard J. Needs, Gora V. Shlyapnikov

Published May 18, 2011• 19 citations
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Abstract

Motivated by potential realizations in cold-atom or cold-molecule systems, we have performed quantum Monte Carlo simulations of two-component gases of fermions in two dimensions with hard-core interactions. We have determined the gross features of the zero-temperature phase diagram by investigating the relative stabilities of paramagnetic and ferromagnetic fluids and crystals. We have also examined the effect of including a pairwise, long-range ${r}^{\ensuremath{-}3}$ potential between the particles. Our most important conclusion is that there is no region of stability for a ferromagnetic fluid phase, even if the long-range interaction is present. We also present results for the pair-correlation function, static structure factor, and momentum density of two-dimensional hard-core fluids.

DOI
10.1103/physrevb.83.195429

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Motivated by potential realizations in cold-atom or cold-molecule systems, we have performed quantum Monte Carlo simulations of two-component gases of fermions in two dimensions with hard-core interactions. We have determined the gross features of the zero-temperature phase diagram by investigating the relative stabilities of paramagnetic and ferromagnetic fluids and crystals. We have also examined the effect of including a pairwise, long-range r\ensuremath−3{r}^{\ensuremath{-}3}r\ensuremath−3 potential between the particles. Our most important conclusion is that there is no region of stability for a ferromagnetic fluid phase, even if the long-range interaction is present. We also present results for the pair-correlation function, static structure factor, and momentum density of two-dimensional hard-core fluids.
Fermionic cold atoms in optical traps provide viable quantum simulators of correlation effects in electronic systems. For dressed Rydberg atoms in two-dimensional traps with out-of-plane dipole moments, a realistic model of the pairwise interaction is of repulsive dipolar 1 / r 3 form at long range, softened to a constant at short range. This study provides parametrizations of fixed-node diffusion Monte Carlo energy data for ferromagnetic (one-component) and paramagnetic (two-component) two-dimensional homogeneous Fermi fluids of interacting dipolar atoms. We find itinerant ferromagnetism to be unstable within our parameter spaces for dipolar interactions both with and without softening. Our parametrization of the energy as a function of density will enable density functional theory to support experimental studies of inhomogeneous fermionic cold-atom systems.
The ground state of a two-dimensional (2D) system of Bose particles of spin zero, interacting via a repulsive Gaussian-core potential, has been investigated by means of quantum Monte Carlo simulations. The quantum phase diagram is qualitatively identical to that of 2D Yukawa bosons. While the system is a fluid at all densities for weak coupling, in the strong-coupling regime it transitions upon compression from a low-density superfluid to a crystal, and then into a reentrant superfluid phase. No evidence of a (supersolid) cluster crystal phase is seen.
We use quantum Monte Carlo methods to calculate the zero-temperature phase diagram of the two-dimensional homogeneous electron gas. We find a transition from a paramagnetic fluid to an antiferromagnetic triangular Wigner crystal at density parameter r(s)=31(1) a.u. and a transition to a ferromagnetic crystal at r(s)=38(5) a.u. The fully spin-polarized fluid is never stable. We search for, but do not find, the ferromagnetic "hybrid" phase proposed by H. Falakshahi and X. Waintal [Phys. Rev. Lett. 94, 046801 (2005)10.1103/PhysRevLett.94.046801].
Variational and diffusion quantum Monte Carlo methods are employed to investigate the zero-temperature phase diagram of the three-dimensional homogeneous electron gas at very low density. Fermi fluid and body-centered cubic Wigner crystal ground-state energies are determined using Slater-Jastrow-backflow and Slater-Jastrow many-body wave functions at different densities and spin polarizations in finite simulation cells. Finite-size errors are removed using twist-averaged boundary conditions and extrapolation of the energy per particle to the thermodynamic limit of infinite system size. Unlike previous studies, our results show that the electron gas undergoes a first-order quantum phase transition directly from a paramagnetic fluid to a body-centered cubic crystal at density parameter rs=86.6(7){r}_{\text{s}}=86.6(7)rs​=86.6(7), with no region of stability for an itinerant ferromagnetic fluid.
We investigate the stability of the Sarma phase in two-component fermion systems in three spatial dimensions. For this purpose we compare strongly-correlated systems with either relativistic or non-relativistic dispersion relation: relativistic quarks and mesons at finite isospin density and spin-imbalanced ultracold Fermi gases . Using a Functional Renormalization Group approach, we resolve fluctuation effects onto the corresponding phase diagrams beyond the mean-field approximation. We find that fluctuations induce a second-order phase transition at zero temperature, and thus a Sarma phase, in the relativistic setup for large isospin chemical potential. This motivates the investigation of the cold atoms setup with comparable mean-field phase structure, where the Sarma phase could then be realized in experiment. However, for the non-relativistic system we find the stability region of the Sarma phase to be smaller than the one predicted from mean-field theory. It is limited to the BEC side of the phase diagram, and the unitary Fermi gas does not support a Sarma phase at zero temperature. Finally, we propose an ultracold quantum gas with four fermion species that has a good chance to realize a zero-temperature Sarma phase.
We study a two-component mixture of fermionic dipoles in two dimensions at zero temperature, interacting via a purely repulsive 1/r31/{r}^{3}1/r3 potential. This model can be realized with ultracold atoms or molecules when their dipole moments are aligned in the confinement direction orthogonal to the plane. We characterize the unpolarized mixture by means of the diffusion Monte Carlo technique. Computing the equation of state, we identify the regime of validity for a mean-field theory based on a low-density expansion and compare our results with the hard-disk model of repulsive fermions. At high density, we address the possibility of itinerant ferromagnetism, namely, whether the ground state can be fully polarized in the fluid phase. Within the fixed-node approximation, we show that the accuracy of Jastrow-Slater trial wave functions, even with the typical two-body backflow correction, is not sufficient to resolve the relevant energy differences. By making use of the iterative-backflow improved trial wave functions, we observe no signature of a fully polarized ground state up to the freezing density.