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arXiv:1011.0055 · Physical Review B

Possible realization of the exciton Bose liquid phase in a hard-core boson model with ring-only exchange interactions

Tiamhock Tay, Olexei I. Motrunich

Published May 17, 2011• 22 citations
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Abstract

We investigate a hard-core boson model with ring-only exchanges on a square lattice, where a ${K}_{1}$ term acts on 1$\ifmmode\times\else\texttimes\fi{}$1 plaquettes and a ${K}_{2}$ term acts on 1$\ifmmode\times\else\texttimes\fi{}$2 and 2$\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 ${K}_{2}$, a valence bond solid for intermediate ${K}_{2}$, and possibly for large ${K}_{2}$ the EBL phase. Away from half-filling, the EBL phase is present for intermediate ${K}_{2}$ and remains stable for a range of densities below 1/2 before phase separation occurs at lower densities.

DOI
10.1103/physrevb.83.205107

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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.
Motivated by the high-Tc{T}_{c}Tc​ cuprates, we consider a model of bosonic Cooper pairs moving on a square lattice via ring exchange. We show that this model offers a natural middle ground between a conventional antiferromagnetic Mott insulator and the fully deconfined fractionalized phase that underlies the spin-charge separation scenario for high-Tc{T}_{c}Tc​ superconductivity. We show that such ring models sustain a stable critical phase in two dimensions, the exciton Bose liquid (EBL). The EBL is a compressible state, with gapless but uncondensed boson and ``vortex'' excitations, power-law superconducting and charge-ordering correlations, and broad spectral functions. We characterize the EBL with the aid of an exact plaquette duality transformation, which motivates a universal low-energy description of the EBL. This description is in terms of a pair of dual bosonic phase fields, and is a direct analog of the well known one-dimensional bosonization approach. We verify the validity of the low-energy description by numerical simulations of the ring model in its exact dual form. The relevance to the high-Tc{T}_{c}Tc​ superconductors and a variety of extensions to other systems are discussed, including the bosonization of a two-dimensional fermionic ring model.
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 13\frac{1}{3}31​ and 23\frac{2}{3}32​ 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.
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We examine the ground-state phase diagram of repulsively interacting hard-core bosons on the quarter-filled checkerboard lattice using quantum Monte Carlo simulations constrained to the canonical ensemble. At a sufficiently large repulsion, the system undergoes a quantum phase transition from a superfluid into a valence-bond-solid regime. We identify this as a weakly first-order quantum melting transition at quarter filling. Furthermore, by examining appropriate order parameters, we exhibit the mixed nature of the valence bond solid, with both columnar and plaquette long-ranged order. Our results demonstrate the realization of the mixed columnar-plaquette phase found recently for the square lattice quantum dimer model in a microscopic bosonic system.
We examine the superfluid phase of a hard-core boson model with nearest-neighbor exchange JJJ and four-particle ring-exchange KKK at half filling on the square lattice. At zero temperature we find that the uniform superfluid in the pure-JJJ model is quickly destroyed by the inclusion of negative-KKK ring-exchange interactions, favoring a state with a $(\ensuremath{\pi},\ensuremath{\pi})$ ordering wave vector. Minimization of the mean-field energy suggests that another type of superfluid state, characterized by nonzero bond chirality, is formed. We also study the behavior of the finite-TTT Kosterlitz-Thouless phase transition in the uniform superfluid phase, by forcing the Nelson-Kosterlitz universal jump condition on the finite-TTT spin-wave superfluid density. Away from the pure JJJ point, TKT{T}_{KT}TKT​ decreases rapidly for negative KKK, while for positive KKK, TKT{T}_{KT}TKT​ reaches a maximum at some $K\ensuremath{\ne}0$ in agreement with recent quantum Monte Carlo simulations.