XY ring exchange model with frustrated Ising coupling on the triangular lattice

TL;DR

This paper explores a frustrated XY ring-exchange model with Ising coupling on a triangular lattice, revealing how quantum fluctuations lift classical degeneracy and lead to unique gapped excitations, with implications for quantum phase behavior.

Contribution

It introduces a detailed analysis of a $Z_2$-invariant XY ring-exchange model with frustrated Ising interactions, highlighting the effects of quantum fluctuations on ground state degeneracy and excitation spectra.

Findings

Classical ground state degeneracy due to $Z_2$-invariance.

Quantum fluctuations produce a gapped quadratic dispersion near ${\bf k}=0$.

Frustration effects suggest possible emergent quantum phases.

Abstract

We investigate the nature of a $Z_2$-invariant XY ring-exchange interaction with a frustrated Ising coupling on the triangular lattice. In the limit of pure XY ring-exchange interaction, we show that the classical ground state is degenerate resulting from the $Z_2$-invariance of the Hamiltonian. Quantum fluctuations lift these classical degenerate ground states and produce an unusual state whose excitation spectrum exhibits a gapped maximum quadratic dispersion near ${\bf k}=0$ and vanishes at the midpoints of each side of the Brillouin zone. This result is in contrast to a gapless quadratic dispersion near ${\bf k}=0$ in the U(1)-invariant counterpart. We also study the effects of frustration when competing with a classically frustrated Ising interaction. We provide a glimpse into the possible quantum phases that could emerge. A comprehensive understanding of this Hamiltonian, however, cannot be elucidated analytically and requires an explicit numerical simulation.