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.
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.
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.
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.
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- 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 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.
Recent numerical work [Z. Y. Meng et al., Nature (London) 464, 847 (2010)] indicates the existence of a spin liquid (SL) phase that intervenes between the antiferromagnetic and semimetallic phases of the half filled Hubbard model on a honeycomb lattice. To better understand the nature of this exotic phase, we study the quantum J(1)-J(2) spin model on the honeycomb lattice, which provides an effective description of the Mott insulating region of the Hubbard model. Employing the variational Monte Carlo approach, we analyze the phase diagram of the model. We find three phases-antiferromagnetic, an unusual Z(2) SL state, and a dimerized state with spontaneously broken rotational symmetry. We identify the Z(2) SL state as the likely candidate for the SL phase of the Hubbard model.
In this thesis, the Hubbard model with hopping amplitude, t, and on-site interaction, U, in the Mott-insulating regime is explored for unconventional magnetic phases at T = 0 K. These phases are captured within effective low-energy descriptions, and are triggered by quantum fluctuations due to finite hopping. We aim for unconventional phases from two mechanisms, an increased symmetry SU(N) with N > 2 compared to the most common SU(2), and highly frustrated interactions. For SU(N)-symmetric fermions in artificial gauge fields, chiral spin liquid phases (CSLs) are investigated. They are determined within effective spin models, which we derive in order six in t/U for the honeycomb lattice for general values of N, and study in detail for the triangular lattice up to order five in t/U for SU(3) and SU(7) by exact diagonalisations and variational Monte Carlo simulations. On the triangular lattice, the third-order effective model is the J -K model with nearest-neighbour coupling, J ∈ R, and ring exchange, K ∈ C. For SU(3) and Im K = 0, the three-sublattice long-range ordered phase is ruled out by a spontaneously time-reversal symmetry breaking π/3-flux CSL through � nite hopping. Further, for Im K = 0, a lattice nematic, a 120◦ long-ranged ordered, and the ferromagnetically ordered phase occur. The CSL is found to be extended to Re K = 0. It is also present in the fourth- and fifth-order model in the most relevant π-flux case, where time-reversal symmetry is spontaneously broken. Together with the estimated metal-insulator transition point at larger hoppings, this CSL is therefore expected to be realised in the SU(3) Hubbard model. The analogous CSL is also predicted for SU(7)-symmetric fermions. Experimental realisations with ultra-cold atoms in optical lattices are described. SrCu2(BO3)2 is a highly frustrated quantum magnet. At ambient pressure it is captured by the spin-1/2 Shastry-Sutherland model, which yields the effective strong-coupling description of the associated SU(2) Hubbard model. To describe SrCu2(BO3)2 under higher pressure, we extend the Shastry-Sutherland model by asymmetric coupling strengths, and find that asymmetries of a few percent are sufficient to replace the empty plaquette singlet phase (EPP) of the Shastry-Sutherland model with the filled plaquette singlet phase (FPP) that is found to be identical to a quasi one-dimensional Haldane phase. These results are achieved by series expansions and infinite projected entangled-pair states. The dispersions and dynamic structure factors of both plaquette phases are derived. The EPP naturally hosts one low-lying triplon, whereas the FPP has two. Therefore, the FPP appears to be the likely candidate for SrCu2(BO3)2 under pressure. The excitations of both phases show some agreement with experimental data if the exchange amplitudes change more than expected. Further measurements are suggested. At last, an orthogonal-plaquette model of spins-1/2 is introduced and proven to host two exact valence bond crystals based on plaquette singlets with an extensive degeneracy at the phase transition. This model exhibits an extensive number of conserved quantities, which is used for further investigations of the phase diagram.