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arXiv:1206.2566 · Physical Review B

Bose-Hubbard model on a kagome lattice with sextic ring-exchange terms

V. G. Rousseau, Ka-Ming Tam, Mark Jarrell, Juana Moreno

Published Feb 27, 2013• 2 citations
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Abstract

High-order ring-exchange interactions are crucial for the study of quantum fluctuations on many highly frustrated systems. A versatile and efficient quantum Monte Carlo method, which can handle finite and essentially zero temperature and canonical and grand-canonical ensembles, has long been sought. In this paper, we present an exact quantum Monte Carlo study of a model of hard-core bosons with sixth-order ring-exchange interactions on a two-dimensional kagome lattice. By using the stochastic Green function algorithm with global space-time update, we show that the system becomes unstable in the limit of large ring-exchange interactions. It undergoes a phase separation at all fillings, except at $\frac{1}{3}$ and $\frac{2}{3}$ fillings for which the superfluid density vanishes and an unusual mixed valence bond and charge density ordered solid is formed. This explains the universal features seen in previous studies on various different models, such as the transverse-field Ising models, on a kagome lattice near the classical limit.

DOI
10.1103/physrevb.87.075146

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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 large scale quantum Monte Carlo simulations to study an extended Hubbard model of hard core bosons on the kagome lattice. In the limit of strong nearest-neighbor interactions at 1/3 filling, the interplay between frustration and quantum fluctuations leads to a valence bond solid ground state. The system undergoes a quantum phase transition to a superfluid phase as the interaction strength is decreased. It is still under debate whether the transition is weakly first order or represents an unconventional continuous phase transition. We present a theory in terms of an easy plane noncompact CP^{1} gauge theory describing the phase transition at 1/3 filling. Utilizing large scale quantum Monte Carlo simulations with parallel tempering in the canonical ensemble up to 15552 spins, we provide evidence that the phase transition is continuous at exactly 1/3 filling. A careful finite size scaling analysis reveals an unconventional scaling behavior hinting at deconfined quantum criticality.
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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.