# Frustrated honeycomb-lattice bilayer quantum antiferromagnet in a magnetic field: Unconventional phase transitions in a two-dimensional isotropic Heisenberg model

## TL;DR

This paper maps a frustrated bilayer honeycomb quantum antiferromagnet in a magnetic field onto classical models to analyze unconventional phase transitions and spin-flop phenomena at low temperatures.

## Contribution

It introduces a novel mapping of the quantum model onto classical lattice-gas and Ising models, enabling analysis of phase transitions in a frustrated quantum system.

## Key findings

- Finite-temperature order-disorder transition driven by magnetic field
- Indications of a spin-flop like transition in the isotropic model
- Effective classical models accurately describe low-temperature behavior

## Abstract

We consider the spin-1/2 antiferromagnetic Heisenberg model on a bilayer honeycomb lattice including interlayer frustration in the presence of an external magnetic field. In the vicinity of the saturation field, we map the low-energy states of this quantum system onto the spatial configurations of hard hexagons on a honeycomb lattice. As a result, we can construct effective classical models (lattice-gas as well as Ising models) on the honeycomb lattice to calculate the properties of the frustrated quantum Heisenberg spin system in the low-temperature regime. We perform classical Monte Carlo simulations for a hard-hexagon model and adopt known results for an Ising model to discuss the finite-temperature order-disorder phase transition that is driven by a magnetic field at low temperatures. We also discuss an effective-model description around the ideal frustration case and find indications for a spin-flop like transition in the considered isotropic spin model.