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Register a new userTwo-dimensional Mixture of Dipolar Fermions: Equation of State and Magnetic Phases
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We study a two-component mixture of fermionic dipoles in two dimensions at zero temperature, interacting via a purely repulsive $1/r^3$ 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.
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Supersolid phases as a result of a coexistence of superfluid and density ordered checkerboard phases are predicted to appear in ultracold Fermi molecules confined in a bilayer array of two-dimensional square optical lattices. We demonstrate the existence of these phases within the inhomogeneous mean-field approach. In particular, we show that tuning the interlayer separation distance at a fixed value of the chemical potential produces different fractions of superfluid, density ordered, and supersolid phases.
We study the quantum ground state of ultracold bosons in a two-dimensional square lattice. The bosons interact via the repulsive dipolar interactions and s-wave scattering. The dynamics is described by the extended Bose-Hubbard model including correlated hopping due to the dipolar interactions, the coefficients are found from the second quantized Hamiltonian using the Wannier expansion with realistic parameters. We determine the phase diagram using the Gutzwiller ansatz in the regime where the coefficients of the correlated hopping terms are negative and can interfere with the tunneling due to single-particle effects. We show that this interference gives rise to staggered superfluid and supersolid phases at vanishing kinetic energy, while we identify parameter regions at finite kinetic energy where the phases are incompressible. We compare the results with the phase diagram obtained with the cluster Gutzwiller approach and with the results found in one dimension using DMRG.
The liquid-to-ordered phase transition in a bilayer system of fermions is studied within the context of a recently proposed density-functional theory [Phys. Rev. A {bf 92}, 023614 (2015)]. In each two-dimensional layer, the fermions interact via a repulsive, isotropic dipolar interaction. The presence of a second layer introduces an attractive {em interlayer} interaction, thereby allowing for inhomogeneous density phases which would otherwise be energetically unfavourable. For any fixed layer separation, we find an instability to a commensurate one-dimensional stripe phase in each layer, which always precedes the formation of a triangular Wigner crystal. However, at a certain {em fixed} coupling, tuning the separation can lead to the system favoring a commensurate triangular Wigner crystal, or one-dimensional stripe phase, completely bypassing the Fermi liquid state. While other crystalline symmetries, with energies lower than the liquid phase can be found, they are never allowed to form owing to their high energetic cost relative to the triangular Wigner crystal and stripe phase.
We study the emergence of several magnetic phases in dipolar bosonic gases subject to three-body loss mechanism employing numerical simulations based on the density matrix renormalization group(DMRG) algorithm. After mapping the original Hamiltonian in spin language, we find a strong parallelism between the bosonic theory and the spin-1 Heisenberg model with single ion anisotropy and long-range interactions. A rich phase diagram, including ferromagnetic, antiferromagnetic and non-local ordered phases, emerges in the half-filled one-dimensional case, and is preserved even in presence of a trapping potential.
Density-functional theory is utilized to investigate the zero-temperature transition from a Fermi liquid to an inhomogeneous stripe, or Wigner crystal phase, predicted to occur in a one-component, spin-polarized, two-dimensional dipolar Fermi gas. Correlations are treated semi-exactly within the local-density approximation using an empirical fit to Quantum Monte Carlo data. We find that the inclusion of the nonlocal contribution to the Hartree-Fock energy is crucial for the onset of an instability to an inhomogeneous density distribution. Our density-functional theory supports a transition to both a one-dimensional stripe phase, and a triangular Wigner crystal. However, we find that there is an instability first to the stripe phase, followed by a transition to the Wigner crystal at higher coupling.
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