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arXiv:1412.1829 · Physical Review A

Mott-insulator–to–superconductor transition in a two-dimensional superlattice

Rubem Mondaini, Predrag Nikolić, Marcos Rigol

Published Jul 1, 2015• 15 citations
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Abstract

We use quantum Monte Carlo and exact diagonalization calculations to study the Mott-insulator--to--superconductor quantum phase transition in a two-dimensional fermionic Hubbard model with attractive interactions in the presence of a superlattice potential. The model introduced offers unique possibilities to study such transitions in optical lattice experiments. We show that, in regimes with moderate to strong interactions, the transition belongs to the three-dimensional $XY$ universality class. We also explore the character of the lowest-energy charge excitations in the insulating and superconducting phases and show that they can be fermionic or bosonic depending on the parameters chosen.

DOI
10.1103/physreva.92.013601

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We study the superconductor-insulator transition (SIT) in the ground state of the attractive honeycomb Hubbard model in the presence of a staggered potential (a mass term), using a combination of unbiased computational methods, namely, exact diagonalization and quantum Monte Carlo simulations. We probe the nature of the lowest-energy charge excitations across the SIT and show that they are bosonic, as inferred (and shown in the strongly interacting regime) in a previous study of the same model in the square lattice. Increasing the strength of the staggered potential leads to a crossover in which bosonic low-energy excitations give way to fermionic ones within the insulating phase. We also show that the SIT belongs to the 3d3d3d-XY universality class, like in its square lattice counterpart. The robustness of our results in these two lattice geometries supports the expectation that our findings are universal for SITs in clean systems.
We use quantum Monte Carlo simulations and exact diagonalization to explore the phase diagram of the Bose-Hubbard model with an additional superlattice potential. We first analyze the properties of superfluid and insulating phases present in the hard-core limit where an exact analytic treatment is possible via the Jordan-Wigner transformation. The extension to finite on-site interactions is achieved by means of quantum Monte Carlo simulations. We determine insulator and superfluid phase diagrams as functions of the on-site repulsive interaction, superlattice potential strength, and filling, finding that insulators with fractional occupation numbers, which are present in the hard-core case, extend deep into the soft-core region. Furthermore, at integer fillings, we find that the competition between the on-site repulsion and the superlattice potential can produce a phase transition between a Mott insulator and a charge-density-wave insulator, with an intermediate superfluid phase. Our results are relevant to the behavior of ultracold atoms in optical superlattices which are beginning to be studied experimentally.
The zero-temperature universal conductivity of two-dimensional (2D) films at the supeconductor-insulator transition is studied. The existence of a finite conductivity at T=0 and the universality class for this transition is discussed. Neglecting disorder as a first approximation, so the transition is from a commensurate Mott-Hubbard insulator to a superconductor, we calculate analytically the universal conductivity for the 2D pure boson Hubbard model up to the first order in a large-N expansion and numerically by Monte Carlo simulation of the (2+1)-D XY model. From the Monte Carlo results we find the universal conductivity to be ${\mathrm{\ensuremath{\sigma}}}^{\mathrm{*}}$=(0.285\ifmmode\pm\else\textpm\fi{}0.02)${\mathrm{\ensuremath{\sigma}}}_{\mathit{Q}}$, where ${\mathrm{\ensuremath{\sigma}}}_{\mathit{Q}}^{\mathrm{\ensuremath{-}}1}$==RQ{\mathit{R}}_{\mathit{Q}}RQ​==h/(2e)2{)}^{2})2\ensuremath{\approxeq}6.45 k\ensuremath{\Omega}. An analysis in 1D suggests that in the presence of disorder, the universal conductivity in films might be somewhat smaller than this value. The possible existence of universal dissipation in 4He^{4}\mathrm{He}4He films is also discussed briefly.
We study, using quantum Monte Carlo simulations, the bosonic Kondo-Hubbard model in a two-dimensional square lattice. We explore the phase diagram and analyze the mobility of particles and magnetic properties. At unit filling, the transition from a paramagnetic Mott insulator to a ferromagnetic superfluid appears continuous, contrary to what was predicted with mean field. For double occupation per site, both the Mott insulating and superfluid phases are ferromagnetic and the transition is still continuous. Multiband tight-binding Hamiltonians can be realized in optical lattice experiments, which offer not only the possibility of tuning the different energy scales over wide ranges, but also the option of loading the system with either fermionic or bosonic atoms.
We investigate the superconductor-insulator phase transition in the two-dimensional boson Hubbard system with short-range interactions. Fluctuations of both the phase and the amplitude of the superfluid order parameter are included in the determination of the phase diagram at zero and finite temperatures. The mean-field phase boundary is compared to quantum Monte Carlo results. We also calculate the frequency-dependent conductivity in the vicinity of the phase transition and find it universal at the multicritical point.