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arXiv:0706.4310 · Physical Review B

Exotic phase diagram of a cluster charging model of bosons on the kagome lattice

Sergei V. Isakov, Arun Paramekanti, Yong Baek Kim

Published Dec 27, 2007• 21 citations
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Abstract

We study a model of hard-core bosons on the kagome lattice with short-range hopping $(t)$ and repulsive interactions $(V)$. This model directly maps onto an easy-axis $S=1∕2$ XXZ model on the kagome lattice and is also related, at large $V∕t$, to a quantum dimer model on the triangular lattice. Using quantum Monte Carlo numerics, we map out the phase diagram of this model at half-filling. At $T=0$, we show that this model exhibits a superfluid phase at small $V∕t$ and an insulating phase at large $V∕t$, separated by a continuous quantum phase transition at ${V}_{c}∕t\ensuremath{\approx}19.8$. The insulating phase at $T=0$ appears to have no conventional broken symmetries, and is thus a uniform Mott insulator (a ``spin liquid'' in magnetic language). We characterize this insulating phase as a uniform ${Z}_{2}$ fractionalized insulator from the topological order in the ground state and estimate its vison gap. Consistent with this identification, there is no apparent thermal phase transition upon heating the insulator. The insulating phase instead smoothly crosses over into the high temperature paramagnet via an intermediate cooperative paramagnetic regime. We also study the superfluid-to-normal thermal transition for $V<{V}_{c}$. We find that this is a Kosterlitz-Thouless transition at small $V∕t$ but changes to a first order transition for $V$ closer to ${V}_{c}$. We argue that this first order thermal transition is consistent with the presence of a nearby ${Z}_{2}$ insulating ground state obtained from the superfluid ground state by condensing double vortices.

DOI
10.1103/physrevb.76.224431

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We study a model of hard-core bosons on the kagome lattice with short-range hopping (t)(t)(t) and repulsive interactions (V)(V)(V). This model directly maps onto an easy-axis S=1∕2S=1∕2S=1∕2 XXZ model on the kagome lattice and is also related, at large V∕tV∕tV∕t, to a quantum dimer model on the triangular lattice. Using quantum Monte Carlo numerics, we map out the phase diagram of this model at half-filling. At T=0T=0T=0, we show that this model exhibits a superfluid phase at small V∕tV∕tV∕t and an insulating phase at large V∕tV∕tV∕t, separated by a continuous quantum phase transition at Vc∕t\ensuremath≈19.8{V}_{c}∕t\ensuremath{\approx}19.8Vc​∕t\ensuremath≈19.8. The insulating phase at T=0T=0T=0 appears to have no conventional broken symmetries, and is thus a uniform Mott insulator (a ``spin liquid'' in magnetic language). We characterize this insulating phase as a uniform Z2{Z}_{2}Z2​ fractionalized insulator from the topological order in the ground state and estimate its vison gap. Consistent with this identification, there is no apparent thermal phase transition upon heating the insulator. The insulating phase instead smoothly crosses over into the high temperature paramagnet via an intermediate cooperative paramagnetic regime. We also study the superfluid-to-normal thermal transition for V<VcV<{V}_{c}V<Vc​. We find that this is a Kosterlitz-Thouless transition at small V∕tV∕tV∕t but changes to a first order transition for VVV closer to Vc{V}_{c}Vc​. We argue that this first order thermal transition is consistent with the presence of a nearby Z2{Z}_{2}Z2​ insulating ground state obtained from the superfluid ground state by condensing double vortices.
We study a model of hard-core bosons with short-range repulsive interactions at half filling on the kagome lattice. Using quantum Monte Carlo numerics, we find that this model shows a continuous superfluid-insulator quantum phase transition, with exponents z=1z=1z=1 and $\ensuremath{\nu}\ensuremath{\approx}0.67(5)$. The insulator, I∗{\mathcal{I}}^{*}I∗, exhibits short-ranged density and bond correlations, topological order, and exponentially decaying spatial vison correlations, all of which point to a Z2{Z}_{2}Z2​ fractionalized phase. We estimate the vison gap in I∗{\mathcal{I}}^{*}I∗ from the temperature dependence of the energy. Our results, together with the equivalence between hard-core bosons and S=1/2S=1/2S=1/2 spins, provide compelling evidence for a spin-liquid phase in an easy-axis spin-1/21/21/2 model with no special conservation laws.
We study a model of hard-core bosons with short-range repulsive interactions at half filling on the kagome lattice. Using quantum Monte Carlo numerics, we find that this model shows a continuous superfluid-insulator quantum phase transition, with exponents z=1 and nu approximately 0.67(5). The insulator, I*, exhibits short-ranged density and bond correlations, topological order, and exponentially decaying spatial vison correlations, all of which point to a Z2 fractionalized phase. We estimate the vison gap in I* from the temperature dependence of the energy. Our results, together with the equivalence between hard-core bosons and S=1/2 spins, provide compelling evidence for a spin-liquid phase in an easy-axis spin-1/2 model with no special conservation laws.
Using large scale quantum Monte Carlo simulations and dual vortex theory, we analyze the ground state phase diagram of hard-core bosons on the kagome lattice with nearest-neighbor repulsion. In contrast with the case of a triangular lattice, no supersolid emerges for strong interactions. While a uniform superfluid prevails at half filling, two novel solid phases emerge at densities rho=1/3 and rho=2/3. These solids exhibit an only partial ordering of the bosonic density, allowing for local resonances on a subset of hexagons of the kagome lattice. We provide evidence for a weakly first-order phase transition at the quantum melting point between these solid phases and the superfluid.
Using large scale quantum Monte Carlo simulations and dual vortex theory we analyze the ground state phase diagram of hard-core bosons on the kagome lattice with nearest neighbor repulsion. In contrast to the case of a triangular lattice, no supersolid emerges for strong interactions. While a uniform superfluid prevails at half-filling, two novel solid phases emerge at densities ρ=1/3\rho=1/3ρ=1/3 and ρ=2/3\rho=2/3ρ=2/3. These solids exhibit an only partial ordering of the bosonic density, allowing for local resonances on a subset of hexagons of the kagome lattice. We provide evidence for a weakly first-order phase transition at the quantum melting point between these solid phases and the superfluid.
Strongly correlated systems on geometrically frustrated lattices can stabilize a large number of interesting phases that includes a wide array of novel Mott insulators in both bosonic and electronic systems. Charge fluctuations in a Mott insulator are suppressed due to strong mutual interaction among the particles. The presence of frustration is of particular importance as the physics it offers is often rich, unexpectedly complicated, and continues to raise many open questions. The thesis elucidates some of these issues on a kagome lattice where strong interactions among the particles in the Mott phase impose non-trivial local constraints depending on the filling fraction on the lattice. These Mott insulators, in addition to featuring unusual magnetic and/or charge ordering, can also harbor topologically ordered states of quantum matter, e.g., resonating valence bond liquids realized in certain quantum dimer models on non-bipartite lattices. The dimer models can be regarded as low-energy effective theories for different types of bosonic models in the strong-coupling limit. Exploring this connection is a central theme of this thesis with the aim of realizing novel strongly correlated ground states. Past studies of these models have revealed the existence of various ordered and disordered phases with distinct signatures. Among these low-energy phases, the presence of a stable topological liquid at a particular point, known as Rokhsar-Kivelson point, in the phase diagram is notable. The classical versions of the dimer model are also known to have garnered a vast interest in various fields ranging from problems of pure mathematical origin to ones in physical chemistry as well as statistical physics. Pioneered by Kasteleyn, several analytical works came forward to exactly calculate the partition function of the problem from which other physical observables can be derived. Classical numerical methods are extensively applied to these models to verify the analytical predictions. We introduce a new classical algorithm here to compute the correlation functions of a classical dimer model on a square (bipartite) and a triangular (non-bipartite) lattice based on a tensor network construction. The method, called tensor network renormalization group, turns out to be a powerful tool for simulating short-ranged gapped systems as inferred from our results benchmarked against the classical Monte-Carlo technique and compared with past analytical studies. One should note that the quantum dimer model at the Rokhsar-Kivelson point can also be described as an infinite temperature canonical ensemble of classical dimers because of the particular structure of the ground state which is an equal weight superposition in the configuration manifold. The geometry of the lattice plays a pivotal role in deciding the nature of the phases that arise in the dimer models. Many physical properties of the dimer liquid phase can be extracted in the simple classical setting which certainly allows for a deep understanding of the classical models to be developed. The liquid phase is gapped on non-bipartite lattices and gapless on bipartite lattices, which is reflected in the decay of correlation functions with spatial distances. In general on non-bipartite lattices, the topological nature of the dimer liquid is characterized by a Z2 topological order which survives even when the model is perturbed away from the Rokhsar-Kivelson point. Stability of this liquid phase not only depends on the lattice geometries but notably on dimer concentrations also. In this context, we focus on a particular variant of the dimer model on a triangular lattice which is known as the quantum fully packed loop model. The model is composed of nonintersecting closed loops made of dimers and governed by the same Hamiltonian as the quantum dimer model. The loop model provides an effective low-energy description of a strongly correlated bosonic system at 1/3 filling on the kagome lattice. The corresponding Bose-Hubbard Hamiltonian consists of nearest-neighbor hopping and all possible repulsive interactions within a hexagonal plaquette. Conspicuous features of the zero-temperature phase diagram for this model include (i) presence of a stable Z2 liquid even without any Rokhsar-Kivelson potential term (in distinction to the standard quantum dimer model), and (ii) an unconventional phase transition from the liquid phase to a novel crystalline phase that has nematic order (dubbed lattice nematic). For a deeper understanding of the physics, a mapping to an Ising gauge theory is presented. The gauge theoretic description provides a useful way to predict the nature of the quantum phase transition to lie in the O(3) universality class. Finally a fermionic model at the same 1/3 filling is considered in which the ground state exhibits a number of exotic local orderings resulting from the spin-charge interplay of electrons. The Hamiltonian comprises nearest-neighbor hopping, strong on-site Coulomb interaction, and repulsive interaction terms only between nearest-neighbors. In the strong correlation limit, this fermionic problem maps to a two-color fully packed loop model – a model in which the loop segments carry an additional quantum number as color on a honeycomb lattice. The effective theory is governed by coherent three-particle ring exchanges and nearest-neighbor antiferromagnetic spin exchanges. The competition between these two leads to a phase diagram composed of a novel plaquette ordered state (known as the plaquette phase) that undergoes phase transition to a new kind of charge ordered state which we call a short loop phase. From our numerical analysis, we conclude that the plaquette phase features an unusual antiferromagnetic order with gapless spin excitations while the charge-ordered state is subjugated by spin fluctuations of localized electrons arranged in small hexagonal loops on the kagome lattice.
We consider hard-core bosons on the kagome lattice in the presence of short-range repulsive interactions and focus particularly on the filling factor 1/31/31/3. In the strongly interacting limit, the low-energy excitations can be described by the quantum fully packed loop coverings on the triangular lattice. Using a combination of tensor product state based methods and exact diagonalization techniques, we show that the system has an extended Z2{\mathbb{Z}}_{2}Z2​ topological liquid phase as well as a latti ce nematic phase. The latter breaks lattice rotational symmetry. By tuning appropriate parameters in the model, we study the quantum phase transition between the topological and the symmetry broken phases. We construct the critical theory for this transition using a mapping to an Ising gauge theory that predicts the transition to belong to the O(3)O(3)O(3) universality class.