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Quantum Monte Carlo studies of fermions with attractive interactions in optical traps

F. Karim Pour

Published Jan 1, 2008• 0 citations
Publisher

Abstract

About 50 years ago, Penrose and Onsager posed the question: Can a solid be superfluid? Supersolids are defined by the simultaneous presence of two types of long-range order: superfluidity' coexisting with a periodic modulation of the density', in other words, supersolids combine the main characteristics of solids and superfluids. Using quantum Monte Carlo simulations, we show here that density-density and pairing correlation functions of the one-dimensional attractive fermionic Hubbard model in a confinement potential are characterized by the anomalous dimension (Luttinger parameter) of a corresponding periodic system. This allows to determine conditions for a supersolid state inside a trap. We show explicitely, that under such conditions the structure form factors for both correlation functions scale with the same exponent upon increasing the system size, thus giving rise to a (quasi-)supersolid.

DOI
10.18419/opus-4825

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Using quantum Monte Carlo simulations, we show that density-density and pairing correlation functions of the one-dimensional attractive fermionic Hubbard model in a harmonic confinement potential are characterized by the anomalous dimension ${K}_{\ensuremath{\rho}}$ of a corresponding periodic system, and hence display quantum critical behavior. The corresponding fluctuations render the SU(2) symmetry breaking by the confining potential irrelevant, leading to structure form factors for both correlation functions that scale with the same exponent upon increasing the system size, thus giving rise to a (quasi)supersolid.
We investigate two-component ultracold fermionic atoms with attractive interactions trapped in a two-dimensional optical lattice at zero temperature. By introducing a superfluid trial state with spatially modulated order parameters, we perform the variational Monte Carlo simulations to treat the correlation effects beyond mean-field treatments. It is shown that there appears a strong tendency to the formation of a density wave state in the regions with specific values of local atom density. We then analyze two kinds of perturbations to the superfluid state and show that a coexisting state of superfluid and density wave ordering, a sort of supersolid state, can be stabilized. It is discussed how the trap potential and the resulting spatial modulation of the superfluid state affect the momentum distributions and the noise correlation functions.
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We use quantum Monte Carlo simulations to determine the ground state phase diagram of the Bose-Hubbard Hamiltonian with long-range repulsive interactions. At half filling one finds superfluidity and insulating solid phases. Depending on the relative sizes of near-neighbor and next-near-neighbor interactions, this solid follows either a checkerboard or a striped pattern. In neither case is there a coexistence with superfluidity. However, at incommensurate densities ``supersolid'' phases appear with simultaneous diagonal and off-diagonal long-range order.
The supersolid is a long-sought phase in condensed matter physics, characterized by the coexistence of density wave and superfluid orders. This phase is counterintuitive, as different symmetry-breaking orders typically compete with one another. A deeper understanding of how such a state forms in condensed matter systems remains an open question, especially in quasi-one-dimensional correlated systems. In this work, we investigate the emergence of supersolids in Luttinger-Emery liquids using a variational method. As the system consists of coupled Luttinger-Emery liquid chains, we refer to this phase as a quasi-one-dimensional supersolid. Notably, we demonstrate that the quasi-one-dimensional supersolid phase is energetically favorable in chains with finite size or short-range order. Furthermore, we investigate the collective dynamics of these coexisting charge density waves and superconducting states, identifying a quasi-Goldstone mode. Our theory provides valuable insights into both the ground state and the dynamic properties of supersolids in strongly correlated systems.
Using quantum Monte Carlo simulations, we study a mixture of bosons and fermions loaded on an optical lattice. With simple on-site repulsive interactions, this system can be driven into a solid phase. We dope this phase and, in analogy with pure bosonic systems, identify the conditions under which the bosons enter a supersolid phase, i.e., exhibit at the same time charge density-wave and superfluid order. We perform finite-size scaling analysis to confirm the presence of a supersolid phase and discuss its properties, showing that it is a collective phase that also involve phase coherence of the fermions.