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arXiv:1012.4494 · New Journal of Physics

Mott insulators in a fully frustrated Bose–Hubbard model on the honeycomb lattice

Stephen Inglis, Roger G Melko

Published May 13, 2011• 1 citation
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Abstract

We examine the effects of quantum fluctuations on a classical spin liquid state in the fully frustrated honeycomb lattice Bose–Hubbard model in the hard-core limit using quantum Monte Carlo simulations. Frustration is induced explicitly in the model by modulating the sign of the nearest-neighbor interaction spatially around each lattice hexagon. A superfluid-to-Mott insulating quantum phase transition can be induced by varying the relative strength of the classical interaction and quantum hopping. In the cases where the interaction has a regular spatial modulation, hopping promotes a phase transition to a symmetry-broken half-filled valence-bond solid state. When the interaction is forced to have no regular pattern, the insulating state is found to be random and gapped, suggesting the existence of a Mott glass phase.

DOI
10.1088/1367-2630/13/5/053018

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We examine the effects of quantum fluctuations on a classical spin liquid state in the fully frustrated honeycomb lattice Bose–Hubbard model in the hard-core limit using quantum Monte Carlo simulations. Frustration is induced explicitly in the model by modulating the sign of the nearest-neighbor interaction spatially around each lattice hexagon. A superfluid-to-Mott insulating quantum phase transition can be induced by varying the relative strength of the classical interaction and quantum hopping. In the cases where the interaction has a regular spatial modulation, hopping promotes a phase transition to a symmetry-broken half-filled valence-bond solid state. When the interaction is forced to have no regular pattern, the insulating state is found to be random and gapped, suggesting the existence of a Mott glass phase.
We examine the effects of quantum fluctuations on a classical spin liquid state in the fully-frustrated honeycomb lattice Bose Hubbard model using quantum Monte Carlo simulations. Frustration is induced explicitly in the model by modulating the sign of the interaction spatially around each lattice hexagon. A superfluid to Mott insulating quantum phase transition can be induced by varying the relative strength of the classical interaction and quantum hopping. In the cases where the interaction has a regular spatial modulation, hopping promotes a phase transition to a symmetry-broken valence-bond solid state. When the interaction is forced to have no regular pattern, the Mott insulating phase is found to be featureless and gapped, making it an interesting candidate state for a quantum spin liquid arising in a Hamiltonian with only nearest-neighbor interactions.
In this thesis we present results from quantum Monte Carlo for the fully-frustrated honeycomb lattice. \nThe XXZ model is of interest in the classical limit, as there is a mapping between the classical fully-frustrated honeycomb Ising model groundstates and the classical hard-core dimer model groundstate. \nThe aim of this work is to explore the effect of quantum fluctuations on the fully-frustrated honeycomb model to see what sort of interesting physics arises. \nOne might expect unusual physics due to the quantum hard-core dimer model, where interesting physics are known to exist. \nThis is because there is a duality mapping between the classical dimer model and the classical fully-frustrated honeycomb Ising model. \nIndeed, by studying the fully-frustrated honeycomb XXZ model we find that in some cases the system orders into crystal-like structures, a case of order-by-disorder. \nThe most interesting case, when the frustrating bonds are chosen randomly, reveals to us a novel state without any discernible order while at the same time avoiding the freezing one would expect of a glass. \nThis state is a featureless system lacking low temperature magnetic susceptibility---a candidate ``quantum spin liquid''. \nFuture work that might more easily measure quantum spin liquid criteria is suggested.
We consider extended Hubbard models with repulsive interactions on a honeycomb lattice, and the transitions from the semimetal to Mott insulating phases at half-filling. Because of the frustrated nature of the second-neighbor interactions, topological Mott phases displaying the quantum Hall and the quantum spin Hall effects are found for spinless and spin fermion models, respectively. The mean-field phase diagram is presented and the fluctuations are treated within the random phase approximation. Renormalization group analysis shows that these states can be favored over the topologically trivial Mott insulating states.
By using a state-of-the-art tensor network state method, we study the ground-state phase diagram of an extended Bose-Hubbard model on the square lattice with frustrated next-nearest-neighbor tunneling. In the hard-core limit, tunneling frustration stabilizes a peculiar half-supersolid phase with one sublattice being superfluid and the other sublattice being Mott insulator away from half filling. In the soft-core case, the model shows very rich phase diagrams above half filling, including three different types of supersolid phases depending on the interaction parameters. The considered model provides a promising route to experimentally search for a novel stable supersolid state induced by frustrated tunneling in the region below half filling with dipolar atoms or molecules.
The Hubbard model encapsulates the physics of strongly correlated quantum systems in its most basic form. It has been studied intensively in the context of the high-temperature superconductivity. A number of novel phases were recently proposed for Hubbard-like models on the honeycomb lattice, the structure of graphene. We analyzed the Hubbard model of spin- 12\frac{1}{2}21​ fermions on the honeycomb lattice at half-filling using large-scale quantum Monte Carlo simulations. We find that the weak coupling semimetal and the antiferromagnetic Mott insulator at strong interaction are separated by an extended gapped phase in an intermediate coupling regime. Exploring excitation gaps, various correlation functions as well as probing for flux quantization, we conclude that a quantum spin liquid, lacking any conventional order, emerges with local charge and spin correlations, best described by a resonating valence bonds state.
We investigate the ground-state and finite-temperature phase diagrams of the Bose-Hubbard model on a honeycomb superlattice. The interplay between the superlattice potential depth $\mathrm{\ensuremath{\Delta}}/t$ and the on-site interaction U/tU/tU/t gives rise to three distinct quantum phases at zero temperature: a superfluid phase, a Mott insulator I phase with unit filling on each site, and a Mott insulator II phase characterized by density imbalance---double occupancy on one sublattice and vacancy on the other at unit filling. The SF-MI transitions are found to be continuous, consistent with second-order quantum phase transitions. We further extend our analysis to finite temperatures within the superfluid regime. Our work highlights how a honeycomb superlattice geometry enables access to interaction- and lattice-modulation-driven quantum phases, including a density-imbalanced Mott insulator and a robust superfluid regime, offering concrete theoretical predictions for cold-atom experiments.