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Europhysics Letters (EPL)

Phase diagram of disordered two-dimensional extended Bose-Hubbard model

Ji-Ming Gao, Rong-An Tang, Ju-Kui Xue

Published Mar 1, 2017• 4 citations
Publisher

Abstract

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.

DOI
10.1209/0295-5075/117/60007

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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.
We investigate the ground-state phase diagram of the soft-core Bose-Hubbard model with the nearest-neighbor repulsion on a square lattice by using an unbiased quantum Monte Carlo method. In contrast to a previous study [P. Sengupta et al., Phys. Rev. Lett. 94, 207202 (2005)], we present the ground-state phase diagrams up to high hopping amplitudes. As a result, in addition to the known supersolid above half-filling, we find a supersolid phase below and at half-filling for high hopping amplitudes. In addition, for a strong nearest-neighbor repulsion, we show that the supersolid phase occupies a remarkably broad region in the phase diagram. These results are in agreement with the results of the Gutzwiller mean-field approximation [M. Iskin, Phys. Rev. A 83, 051606(R) (2011); T. Kimura, Phys. Rev. A 84, 063630 (2011)]. However, it turns out that the regions of the supersolid phases are significantly smaller than the mean-field results.
We use quantum Monte Carlo simulations with the worm algorithm to study the phase diagram of a two-dimensional Bose-Hubbard model with cavity-mediated long-range interactions and uncorrelated disorder in the hard-core limit. Our study shows the system is in a supersolid phase at weak disorder and a disordered solid phase at stronger disorder. Due to long-range interactions, a large region of metastable states exists in both clean and disordered systems. By comparing the phase diagrams for both clean and disordered systems, we find that disorder suppresses metastable states and superfluidity. We compare these results with the phase diagram of the extended Bose-Hubbard model with nearest-neighbor interactions. Here, the supersolid phase does not exist even at weak disorder. We identify two kinds of glassy phases: a Bose glass phase and a disordered solid phase. The glassy phases intervene between the density-wave and superfluid phases as the Griffiths phase of the Bose-Hubbard model. The disordered solid phase intervenes between the density-wave and Bose glass phases since both have a finite structure factor.
We introduce an inhomogeneous bosonic mixture composed of two kinds of hard-core and semi-hard-core bosons with different nilpotency conditions and demonstrate that in contrast with the standard hard-core Bose-Hubbard model, our bosonic mixture with nearest- and next-nearest-neighbor interactions on a square lattice develops the checkerboard supersolid phase characterized by the simultaneous superfluid and checkerboard solid orders. Our bosonic mixture is created from a two-orbital Bose-Hubbard model including two kinds of bosons: a single-orbital boson and a two-orbital boson. By mapping the bosonic mixture to an anisotropic inhomogeneous spin model in the presence of a magnetic field, we study the ground-state phase diagram of the model by means of cluster mean field theory and linear spin-wave theory and show that various phases such as solid, superfluid, supersolid, and Mott insulator appear in the phase diagram of the mixture. Competition between the interactions and magnetic field causes the mixture to undergo different kinds of first- and second-order phase transitions. By studying the behavior of the spin-wave excitations, we find the reasons of all first- and second-order phase transitions. We also obtain the temperature phase diagram of the system using cluster mean field theory. We show that the checkerboard supersolid phase persists at finite temperature comparable with the interaction energies of bosons.
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.
We study the one-dimensional Bose-Hubbard model using the density-matrix renormalization group. For the cases of on-site interactions and additional nearest-neighbor interactions the phase boundaries of the Mott insulators and charge-density wave phases are determined. We find a direct phase transition between the charge-density wave phase and the superfluid phase, and no supersolid or normal phases. In the presence of nearest-neighbor interaction the charge density wave phase is completely surrounded by a region in which the effective interactions in the superfluid phase are repulsive. In this region a single impurity causes the system to be insulating. An even bigger region of the superfluid phase is driven into a Bose-glass phase by any finite quenched disorder. We determine the boundaries of both regions in the phase diagram. The ac conductivity of the superfluid phase in the attractive and the repulsive region is calculated, and a big superfluid stiffness is found in the attractive as well as the repulsive region.
We use quantum Monte Carlo simulations to study the effect of disorder, in the form of a disordered chemical potential, on the phase diagram of the hard-core Bosonic Hubbard model in two dimensions. We find numerical evidence that in two dimensions, no matter how weak the disorder, it will always destroy the long-range density wave order (checkerboard solid) present at half filling and strong nearest-neighbor repulsion and replace it with a bose glass phase. We study the properties of this glassy phase including the superfluid density, energy gaps, and the full Green's function. We also study the possibility of other localized phases at weak nearest-neighbor repulsion, i.e., Anderson localization. We find that such a phase does not truly exist: The disorder must exceed a threshold before the bosons (at weak nearest-neighbor repulsion) are localized. The phase diagram for hard-core bosons with disorder cannot be obtained easily from the soft-core phase diagram discussed in the literature.