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arXiv:cond-mat/0505347 · Physical Review B

Ring exchange and phase separation in the two-dimensional boson Hubbard model

V. G. Rousseau, Richard T. Scalettar, G. G. Batrouni

Published Aug 26, 2005• 19 citations
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Abstract

We present quantum Monte Carlo simulations of the soft-core Bosonic Hubbard model with a ring exchange term $K$. For values of $K$ which exceed roughly half the on-site repulsion $U$, the density is a nonmonotonic function of the chemical potential, indicating that the system has a tendency to phase separate. This behavior is confirmed by an examination of the density-density structure factor at small momenta and real-space images of the boson configurations. Adding a near-neighbor repulsion can compete with phase separation, but still does not give rise to a stable normal Bose liquid.

DOI
10.1103/physrevb.72.054524

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We present quantum Monte Carlo simulations of the soft-core Bosonic Hubbard model with a ring exchange term KKK. For values of KKK which exceed roughly half the on-site repulsion UUU, the density is a nonmonotonic function of the chemical potential, indicating that the system has a tendency to phase separate. This behavior is confirmed by an examination of the density-density structure factor at small momenta and real-space images of the boson configurations. Adding a near-neighbor repulsion can compete with phase separation, but still does not give rise to a stable normal Bose liquid.
We present a quantum Monte Carlo study of a hard-core boson model with ring-only exchanges on a square lattice, where a K1 term acts on 1×1 plaquettes and a K2 term acts on 1×2 and 2×1 plaquettes. At half-filling, the phase diagram reveals charge density wave for small K2, valence bond solid for intermediate K2, and possibly for large K2 the novel exciton Bose liquid (EBL) phase first proposed by Paramekanti et al [Phys. Rev. B 66, 054526 (2002)10.1103/PhysRevB.66.054526]. Away from half-filling, the EBL phase is present already for intermediate K2 and remains stable for a range of densities below 1/2 before phase separation sets in at lower densities.
We investigate a hard-core boson model with ring-only exchanges on a square lattice, where a K1{K}_{1}K1​ term acts on 1$\ifmmode\times\else\texttimes\fi{}$1 plaquettes and a K2{K}_{2}K2​ term acts on 1$\ifmmode\times\else\texttimes\fi{}2and22 and 22and2\ifmmode\times\else\texttimes\fi{}$1 plaquettes, with a goal of realizing a novel exciton Bose liquid (EBL) phase first proposed by Paramekanti et al. [Phys. Rev. B 66, 054526 (2002)]. We construct Jastrow-type variational wave functions for the EBL, study their formal properties, and then use them as seeds for a projective quantum Monte Carlo study. Using the Green's function Monte Carlo approach, we obtain an unbiased phase diagram that at half-filling reveals a charge density wave for small K2{K}_{2}K2​, a valence bond solid for intermediate K2{K}_{2}K2​, and possibly for large K2{K}_{2}K2​ the EBL phase. Away from half-filling, the EBL phase is present for intermediate K2{K}_{2}K2​ and remains stable for a range of densities below 1/2 before phase separation occurs at lower densities.
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.
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.