Valence-Bond Order in a Honeycomb Antiferromagnet Coupled to Quantum Phonons

TL;DR

This study uses quantum Monte Carlo simulations to show that coupling a honeycomb antiferromagnet to quantum phonons can induce a transition from a Neel state to a Kekule9 valence-bond-solid state, revealing tunable quantum phase transitions.

Contribution

It demonstrates that quantum phonon coupling can induce Kekule9 order and alter phase transitions in a honeycomb antiferromagnet, a novel insight into phonon-spin interactions.

Findings

Coupling to quantum phonons destroys Neel order.

Induces a first-order transition to Kekule9 valence-bond-solid state.

Transition can be tuned by interaction retardation.

Abstract

We use exact quantum Monte Carlo simulations to demonstrate that the N\'eel ground state of an antiferromagnetic SU(2) spin-$\frac{1}{2}$ Heisenberg model on the honeycomb lattice can be destroyed by a coupling to quantum phonons. We find a clear first-order transition to a valence-bond-solid state with Kekul\'e order instead of a deconfined quantum critical point. However, quantum lattice fluctuations can drive the transition towards weakly first-order, revealing a tunability of the transition by the retardation of the interaction. In contrast to the one-dimensional case, our phase diagram in the adiabatic regime is qualitatively different from the frustrated $J_1$-$J_2$ model. Our results suggest that a coupling to bond phonons can induce Kekul\'e order in Dirac systems.