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

TL;DR

This paper investigates a kagome lattice boson model revealing a rich phase diagram with a superfluid phase, a topologically ordered $Z_2$ insulator, and complex thermal transitions, using quantum Monte Carlo simulations.

Contribution

It uncovers a novel $Z_2$ fractionalized insulator phase and details the quantum and thermal phase transitions in a kagome lattice boson model.

Findings

Identification of a $Z_2$ topological insulator with no broken symmetry.

Continuous quantum phase transition at $V_c/t \\approx 19.8$.

Thermal transition from superfluid to normal state varies from Kosterlitz-Thouless to first order.

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 on to 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 (QMC) 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 $V_c/t \approx 19.8$. 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.