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arXiv:1110.2957 · Physical Review B

Percolation-enhanced supersolids in the extended Bose-Hubbard model

Bhargav Kemburi, V. W. Scarola

Published Jan 4, 2012• 14 citations
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Abstract

We theoretically study the stability of lattice supersolid states in the extended Bose-Hubbard model with bounded spatial disorder. We construct a disorder mean-field theory and compare with quantum Monte Carlo calculations. The supersolid survives weak disorder on the simple cubic lattice. We also find that increasing disorder strength can transform a lattice solid into a supersolid as it tends to percolate through the disorder landscape.

DOI
10.1103/physrevb.85.020501

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We theoretically study the stability of lattice supersolid states in the extended Bose-Hubbard model with bounded spatial disorder. We construct a disorder mean-field theory and compare with quantum Monte Carlo calculations. The supersolid survives weak disorder on the simple cubic lattice. We also find that increasing disorder strength can transform a lattice solid into a supersolid as it tends to percolate through the disorder landscape.
The extended Bose-Hubbard model captures the essential properties of a wide variety of physical systems including ultracold atoms and molecules in optical lattices, Josephson junction arrays, and certain narrow band superconductors. It exhibits a rich phase diagram including a supersolid phase where a lattice solid coexists with a superfluid. We use quantum Monte Carlo to study the supersolid part of the phase diagram of the extended Bose-Hubbard model on the simple cubic lattice. We add disorder to the extended Bose-Hubbard model and find that the maximum critical temperature for the supersolid phase tends to be suppressed by disorder. But we also find a narrow parameter window in which the supersolid critical temperature is enhanced by disorder. Our results show that supersolids survive a moderate amount of spatial disorder and thermal fluctuations in the simple cubic lattice.
By using the inhomogeneous mean-field theory, the phase diagram of the two-dimensional soft-core extended Bose-Hubbard model with both on-site and nearest-neighbor interactions in the presence of spatial disorder is determined. Rich phases, including Mott-insulator, checkerboard solid, supersolid, superfluid and disordered solid are obtained. Interestingly, due to the presence of disorder, a new disordered solid phase is found between the incompressible lobes, and it is demonstrated that the supersolid phase can survive in two-dimensional soft-core bosons. Furthermore, the system undergoes the phase transition from a disordered solid into a solid order or supersolid landscape when the disorder strength is increased. For weak nearest-neighbor repulsion, the increase of the disorder strength induces both checkerboard solid and supersolid phases shrinking to smaller hopping regions. However, for strong nearest-neighbor repulsion, the disorder stabilizes the supersolid phase and makes it occupying a remarkably broad region in the phase diagram. The analytical expressions for the phase boundaries between the incompressible and compressible phases are also obtained, which are in qualitative agreement with our numerical results.
The extended Bose-Hubbard model captures the essential properties of a wide variety of physical systems including ultracold atoms and molecules in optical lattices, josephson junction arrays, and narrow band superconductors. It exhibits a rich phase diagram including a supersolid phase where a lattice solid coexists with a superfluid. We use quantum Monte Carlo to map out the phase diagram of the extended Bose-Hubbard model on the simple cubic lattice where the supersolid is expected. We find that the supersolid is very delicate because unexpected phase separated states compete with the supersolid. We add disorder to the extended Bose-Hubbard model and find that the supersolid phase is enhanced by disorder as phase separation is suppressed. Our results establish optimal regimes for observing supersolids and therefore have important implications for their observation.
We study the finite temperature properties of the extended Bose-Hubbard model on a cubic lattice. This model exhibits the so-called supersolid state. To start with, we investigate the ground-state phase diagram and find the supersolid state in the region of underdoped (less than the half-filled) density in contrast to the cases of one- and two-dimensional systems where the superfluid state and the solid state show the phase separation. Next, we investigate ordering processes at finite temperatures by quantum Monte Carlo simulations and find successive superfluid and solid phase transitions. There, we find that the two order parameters compete with each other. We establish a finite temperature phase diagram, which contains the superfluid, the solid, the supersolid, and the disordered phases. We develop a mean-field theory to analyze the ordering processes and compare the result with that obtained by simulations and discuss the mechanism of the competition of these two orders. We also study how the supersolid region shrinks as the on-site repulsion becomes strong.
We study the extended Bose-Hubbard model on a two-dimensional honeycomb lattice by using large-scale quantum Monte Carlo simulations. We present the ground-state phase diagrams for both the hard-core and the soft-core bosons. For the hard-core case, the transition between the $\ensuremath{\rho}=1∕2$ solid and the superfluid is first order, and the supersolid state is unstable toward phase separation. For the soft-core case, due to the presence of multiple occupation, a stable particle-induced supersolid (SS-p) phase emerges when $1∕2<\ensuremath{\rho}<1$. The transition from the solid at $\ensuremath{\rho}=1∕2$ to the SS-p phase is second order with the superfluid density scaling as ${\ensuremath{\rho}}_{s}\ensuremath{\sim}\ensuremath{\rho}\ensuremath{-}1∕2$. The SS-p phase has the same diagonal order as the solid at $\ensuremath{\rho}=1∕2$. As the chemical potential increases further, the SS-p phase turns into a solid where two bosons occupy each site of one sublattice through a first-order transition. We also calculate the critical exponents of the transition between the $\ensuremath{\rho}=1∕2$ solid and superfluid at the Heisenberg point for the hard-core case. We find the dynamical critical exponent z=0.15z=0.15z=0.15, which is smaller than results obtained on smaller lattices. This indicates that zzz approaches zero in the thermodynamic limit, and thus the transition is also first order even at the Heisenberg point.
The introduction of disorder in the extended Bose-Hubbard model gives rise to new glassy quantum phases, namely the Bose-glass and disordered solid phases. In this work, we present a rich phase diagram of interacting bosons in a disordered two-dimensional optical lattice, modeled by the disordered Bose-Hubbard model. We systematically probe the effect of long-range interaction truncated to the nearest neighbors and next-nearest neighbors on the phase diagram. We investigate the zero-temperature ground-state quantum phases using the single-site Gutzwiller mean-field theory. We also employ strong-coupling perturbative expansion to identify the nature of ground-state solid phases analytically. At sufficiently high disorder strength, we observe a quantum phase transition between the disordered solid and Bose-glass phases. We have investigated this transition in greater detail using cluster Gutzwiller mean-field theory to study the effect of intersite correlations which is absent in the single-site Gutzwiller mean-field theory. We have also studied this phase transition from the perspective of percolation theory.