Quantum disordered ground state for hard-core bosons on the frustrated square lattice

TL;DR

This paper explores the phase diagram of hard-core bosons on a frustrated square lattice, revealing a quantum disordered ground state with no long-range order in certain regimes, and identifying various classical and quantum phases.

Contribution

It demonstrates the existence of a quantum disordered ground state in a frustrated square lattice model of hard-core bosons, expanding understanding of quantum phases in such systems.

Findings

No long-range order detected in the quantum disordered phase

Classical ordered phases include Néel and collinear antiferromagnetic states

Quantum disordered state characterized by exponential decay of correlations

Abstract

We investigate the phase diagram of hard-core bosons on a square lattice with competing interactions. The hard-core bosons can be represented also by spin-1/2 operators and the model can therefore be mapped onto an anisotropic $J_1$-$J_2$-Heisenberg model. We find the N\'eel state and a collinear antiferromagnetic state as classical ordered phases to be suppressed for small ferromagnetic exchange terms $J_{1,2}^{x,y}$ and a ferromagnetic phase which orders in the x-y-plane for large $J_{1,2}^{x,y}$. For an intermediate regime the emergence of new quantum states like valence bond crystals or super-solids is predicted for similar models. We do not observe any signal for long-range order in terms of conventional order or dimer correlations in our model and find an exponential decay in the spin correlations. Hence, all evidence is pointing towards a quantum disordered ground state for a small region in the phase diagram.