Quantum phase transitions in the Triangular-lattice Bilayer Heisenberg Model

TL;DR

This paper investigates quantum phase transitions in the triangular-lattice bilayer Heisenberg model, identifying critical points and universality classes for different coupling regimes using expansion methods.

Contribution

It provides the first detailed analysis of phase transitions and universality classes in this specific bilayer model with both ferro- and antiferromagnetic couplings.

Findings

Phase transition at λ_c=-0.2636 for negative λ, in the 3D classical Heisenberg class.

Transition at λ_c≈1.2 for positive λ, consistent with Kawamura's 3D antiferromagnetic stacked triangular lattice.

Spectral weight remains finite at the transition, indicating no free spinon phase.

Abstract

We study the triangular lattice bilayer Heisenberg model with antiferromagnetic interplane coupling $J_\perp$ and nearest neighbour intraplane coupling $J= \lambda J_\perp$, which can be ferro- or antiferromagnetic, by expansions in $\lambda$. For negative $\lambda$ a phase transition is found to an ordered phase at a critical $\lambda_c=-0.2636 \pm 0.0001$ which is in the 3D classical Heisenberg universality class. For $\lambda>0$, we find a transition at a rather large $\lambda_c\approx 1.2$. The universality class of the transition is consistent with that of Kawamura's 3D antiferromagnetic stacked triangular lattice. The spectral weight for the triplet excitations, at the ordering wavevector, remains finite at the transition, suggesting that a phase with free spinons does not exist in this model.