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

S. A. Owerre

doi:10.1016/j.ssc.2016.04.003

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arXiv · 1603.04208

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

S. A. Owerre

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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.

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S. A. Owerre. 2016-04-18. XY ring exchange model with frustrated Ising coupling on the triangular lattice. https://doi.org/10.1016/j.ssc.2016.04.003

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