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arXiv:0811.1224 · Physical Review B

Superfluid phases of lattice bosons with ring-exchange interaction

Robert Schaffer, A. A. Burkov, Roger G. Melko

Published Jul 7, 2009• 10 citations
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Abstract

We examine the superfluid phase of a hard-core boson model with nearest-neighbor exchange $J$ and four-particle ring-exchange $K$ at half filling on the square lattice. At zero temperature we find that the uniform superfluid in the pure-$J$ model is quickly destroyed by the inclusion of negative-$K$ 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-$T$ Kosterlitz-Thouless phase transition in the uniform superfluid phase, by forcing the Nelson-Kosterlitz universal jump condition on the finite-$T$ spin-wave superfluid density. Away from the pure $J$ point, ${T}_{KT}$ decreases rapidly for negative $K$, while for positive $K$, ${T}_{KT}$ reaches a maximum at some $K\ensuremath{\ne}0$ in agreement with recent quantum Monte Carlo simulations.

DOI
10.1103/physrevb.80.014503

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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 (\ensuremathπ,\ensuremathπ)(\ensuremath{\pi},\ensuremath{\pi})(\ensuremathπ,\ensuremathπ) 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≠0K\ensuremath{\ne}0K\ensuremath=0 in agreement with recent quantum Monte Carlo simulations.
We present the linear spin wave theory calculation of the superfluid phase of a hard-core boson J-K model with nearest neighbour exchange J and four-particle ring-exchange K at half filling on the triangular lattice, as well as the phase diagrams of the system at zero and finite temperatures. A similar analysis has been done on a square lattice (Schaffer et al. Phys. Rev. B, 80, 014503 (2009)). We find similar behaviour to that of a square lattice but with different spin wave values of the thermodynamic quantities. We also find that the pure J model (XY model), which has a well-known uniform superfluid phase with an ordered parameter [Formula: see text] at zero temperature is quickly destroyed by the inclusion of negative-K ring-exchange interactions, favouring a state with a (4π/3, 0) ordering wavevector. We further study the behaviour of the finite-temperature Kosterlitz–Thouless phase transition (TKT) in the uniform superfluid phase, by forcing the universal quantum jump condition on the finite-temperature spin wave superfluid density. We find that for K < 0, the phase boundary monotonically decreases to T = 0 at K/J = −4/3, where a phase transition is expected and TKT decreases rapidly, while for positive K, TKT reaches a maximum at some K ≠ 0. It has been shown on a square lattice using quantum Monte Carlo (QMC) simulations that for small K > 0 away from the XY point, the zero-temperature spin stiffness value of the XY model is decreased (Melko and Sandvik. Ann. Phys. 321, 1651 (2006)). Our result seems to agree with this trend found in QMC simulations for two-dimensional systems.
We study the zero-temperature phase diagram of two-dimensional hard-core bosons on a square lattice with nearest-neighbor and plaquette (ring-exchange) hoppings, at arbitrary densities, by means of a hierarchical mean-field theory. In the frustrated regime, where quantum Monte Carlo suffers from a sign problem, we find a rich phase diagram where exotic states with nonzero chirality emerge. Among them, novel insulating phases, characterized by nonzero bond-chirality and plaquette order, are found over a large region of the parameter space. In the unfrustrated regime, the hierarchical mean-field approach improves over the standard mean-field treatment as it is able to capture the transition from a superfluid to a valence bond state upon increasing the strength of the ring-exchange term, in qualitative agreement with quantum Monte Carlo results.
We study hard-core bosons on the checkerboard lattice with nearest-neighbor unfrustrated hopping ttt and ``tetrahedral'' plaquette charging energy UUU. Analytical arguments and quantum Monte Carlo simulations lead us to the conclusion that the system undergoes a zero temperature (T)(T)(T) quantum phase transition from a superfluid phase at small U∕tU∕tU∕t to a large U∕tU∕tU∕t Mott insulator phase with $\ensuremath{\rho}=1∕4$ for a range of values of the chemical potential $\ensuremath{\mu}$. Further, the quarter-filled insulator breaks lattice translation symmetry in a characteristic fourfold ordering pattern and occupies a lobe of finite extent in the $\ensuremath{\mu}\text{\ensuremath{-}}U∕t$ phase diagram. A quantum Monte Carlo study slightly away from the tip of the lobe provides evidence for a direct weakly first-order superfluid insulator transition away from the tip of the lobe. While analytical arguments lead us to conclude that the transition at the tip of the lobe belongs to a different Landau-forbidden second-order universality class, an extrapolation of our numerical results suggests that the size of the first-order jump does not go to zero even at the tip of the lobe.
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.
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.
Quantum Monte Carlo simulations are used to investigate the two-dimensional superfluid properties of the hard-core boson model, which show a strong dependence on particle density and disorder. We obtain further evidence that a half-filled clean system becomes superfluid via a finite-temperature Kosterlitz-Thouless transition. The relationship between low-temperature superfluid density and particle density is symmetric and appears parabolic about the half filling point. Disorder appears to break the superfluid phase up into two distinct localized states, depending on the particle density. We find that these results strongly correlate with the results of several experiments on high-Tc{\mathit{T}}_{\mathit{c}}Tc​ superconductors.