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AIP conference proceedings

Phase separation in the two-dimensional boson Hubbard model with ring exchange

V. G. Rousseau

Published Jan 1, 2006• 0 citations
Publisher

Abstract

We present quantum Monte Carlo simulations of the soft‐core bosonic Hubbard model with a ring exchange term K. It is argued in litterature that ring exchange processes could give rise to a Bose liquid, a normal liquid compressible but non‐superfluid. However we show that, 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.

DOI
10.1063/1.2178046

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We present quantum Monte Carlo simulations of the soft‐core bosonic Hubbard model with a ring exchange term K. It is argued in litterature that ring exchange processes could give rise to a Bose liquid, a normal liquid compressible but non‐superfluid. However we show that, 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.
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 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 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.
Ring-exchange interactions have been proposed as a possible mechanism for a Bose-liquid phase at zero temperature, a phase that is compressible with no superfluidity. Using the stochastic Green function algorithm (SGF), we study the effect of these interactions for bosons on a two-dimensional triangular lattice. We show that the supersolid phase that is known to exist in the ground state for a wide range of densities is rapidly destroyed as the ring-exchange interactions are turned on. We establish the ground-state phase diagram of the system, which is characterized by the absence of the expected Bose-liquid phase.