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arXiv:1505.05998 · Physical Review B

Z2 topological liquid of hard-core bosons on a kagome lattice at 1/3 filling

Krishanu Roychowdhury, Subhro Bhattacharjee, Frank Pollmann

Published Aug 26, 2015• 30 citations
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Abstract

We consider hard-core bosons on the kagome lattice in the presence of short-range repulsive interactions and focus particularly on the filling factor $1/3$. 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 ${\mathbb{Z}}_{2}$ 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 $O(3)$ universality class.

DOI
10.1103/physrevb.92.075141

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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.
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 ${V}_{c}∕t\ensuremath{\approx}19.8$. 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.
Extend of the Z2\mathbb{Z}_2Z2​-spin liquid phase on the Kagomé-lattice
The Z2\mathbb{Z}_2Z2​ topological phase in the quantum dimer model on the Kagomé-lattice is a candidate for the description of the low-energy physics of the anti-ferromagnetic Heisenberg model on the same lattice. We study the extend of the topological phase by interpolating between the exactly solvable parent Hamiltonian of the topological phase and an effective low-energy description of the Heisenberg model in terms of a quantum-dimer Hamiltonian. Therefore, we perform a perturbative treatment of the low-energy excitations in the topological phase including free and interacting quasi-particles. We find a phase transition out of the topological phase far from the Heisenberg point. The resulting phase is characterized by a spontaneously broken rotational symmetry and a unit cell involving six sites.
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.
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.