Quantum disorder in the spatially completely anisotropic triangular lattice II: frustrated hard-core bosons

TL;DR

This paper investigates quantum disordered phases in a highly anisotropic triangular lattice model with antiferromagnetic XY interactions, revealing continuous connections between phases and potential chiral order, providing insights into quantum spin liquids.

Contribution

It introduces the SCATL model as a generalization of SATL, analyzing its phase diagram with spin-wave theory and exact diagonalizations, highlighting the role of anisotropy in quantum disordered phases.

Findings

Two types of order are separated by non-magnetic phases.

Gapped, disordered phases are continuously connected via anisotropy.

Chiral correlations may persist in some disordered phases.

Abstract

Spin liquids occuring in 2D frustrated spin systems were initially assumed to appear at strongest frustration, but evidence grows that they more likely intervene at transitions between two different types of order. To identify if this is more general, we here analyze a generalization of the spatially anisotropic triangular lattice (SATL) with antiferromagnetic XY interactions, the spatially \emph{completely} anisotropic triangular lattice (SCATL). This model can be implemented in experiments with trapped ions, ultra-small Josephson junctions, or ultracold atoms in optical lattices. Using Takahashi's modified spin-wave theory, we find indications that indeed two different kinds of order are always separated by phases without magnetic long-range order. Our results further suggest that two gapped, magnetically-disordered phases, identified as distinct in the SATL, are actually continuously connected via the additional anisotropy of the SCATL. As these results indicate, this additional anisotropy -- allowing to approach quantum-disordered phases from different angles -- can give fundamental insight into the nature of quantum disordered phases. We complement our results by exact diagonalizations, which also indicate that in part of the gapped non-magnetic phase, chiral long-range correlations could survive.