Staircase of crystal phases of hard-core bosons on the Kagome lattice

TL;DR

This paper investigates the phase diagram of hard-core bosons on the Kagome lattice, revealing a staircase of crystal phases and superfluid transitions influenced by frustration, with implications for quantum magnetism and frustrated systems.

Contribution

It introduces a detailed analysis of crystal and superfluid phases in the Kagome lattice system using hierarchical mean field theory and exact diagonalization, highlighting the role of frustration and classical degeneracy.

Findings

Identification of crystal phases at densities 1/3 and 2/3

Observation of a staircase of crystal phases at various densities

Superfluid phase with chiral currents near half-filling

Abstract

We study the quantum phase diagram of a system of hard-core bosons on the Kagome lattice with nearest-neighbor repulsive interactions, for arbitrary densities, by means of the hierarchical mean field theory and exact diagonalization techniques. This system is isomorphic to the spin S=1/2 XXZ model in presence of an external magnetic field, a paradigmatic example of frustrated quantum magnetism. In the non-frustrated regime, we find two crystal phases at densities 1/3 and 2/3 that melt into a superfluid phase when increasing the hopping amplitude, in semi-quantitative agreement with quantum Monte Carlo computations. In the frustrated regime and away from half-filling, we find a series of plateaux with densities commensurate with powers of 1/3. The broader density plateaux (at densities 1/3 and 2/3) are remnants of the classical degeneracy in the Ising limit. For densities near half-filling, this staircase of crystal phases melts into a superfluid, which displays finite chiral currents when computed with clusters having an odd number of sites. Both the staircase of crystal phases and the superfluid phase prevail in the non-interacting limit, suggesting that the lowest dispersionless single-particle band may be at the root of this phenomenon.