Quantum order by disorder in the Kitaev model on a triangular lattice

TL;DR

This paper investigates how quantum fluctuations lift degeneracy in a triangular lattice Kitaev model, revealing a quantum order-by-disorder mechanism that selects a unique ground state through emergent interactions and hidden symmetries.

Contribution

It demonstrates the quantum order-by-disorder effect in a triangular Kitaev model, showing how quantum fluctuations select a specific ground state from a classically degenerate manifold.

Findings

Quantum fluctuations couple next-nearest-neighbor chains via a four-spin interaction.

Nearest-neighbor chains remain decoupled due to frustration.

A hidden symmetry protects the remaining discrete degeneracy.

Abstract

We identify and discuss the ground state of a quantum magnet on a triangular lattice with bond-dependent Ising-type spin couplings, that is, a triangular analog of the Kitaev honeycomb model. The classical ground-state manifold of the model is spanned by decoupled Ising-type chains, and its accidental degeneracy is due to the frustrated nature of the anisotropic spin couplings. We show how this subextensive degeneracy is lifted by a quantum order-by-disorder mechanism and study the quantum selection of the ground state by treating short-wavelength fluctuations within the linked cluster expansion and by using the complementary spin-wave theory. We find that quantum fluctuations couple next-nearest-neighbor chains through an emergent four-spin interaction, while nearest-neighbor chains remain decoupled. The remaining discrete degeneracy of the ground state is shown to be protected by a hidden symmetry of the model.