Emergent Ising degrees of freedom in frustrated two-leg ladder and bilayer $s=1/2$ Heisenberg antiferromagnets

TL;DR

This study maps low-energy quantum spin degrees of freedom in frustrated two-leg ladder and bilayer antiferromagnets onto classical lattice-gas models, revealing a low-temperature Ising phase transition in the bilayer system.

Contribution

It introduces a novel mapping of quantum Heisenberg antiferromagnets onto classical models, enabling detailed thermodynamic analysis and identifying a new Ising universality class transition.

Findings

Classical lattice-gas models accurately describe quantum thermodynamics up to high temperatures.

A low-temperature phase transition in the bilayer system belongs to the 2D Ising universality class.

The mapping provides a new framework for understanding frustrated quantum spin systems.

Abstract

Based on exact diagonalization data for finite quantum Heisenberg antiferromagnets on two frustrated lattices (two-leg ladder and bilayer) and analytical arguments we map low-energy degrees of freedom of the spin models in a magnetic field on classical lattice-gas models. Further we use transfer-matrix calculations and classical Monte Carlo simulations to give a quantitative description of low-temperature thermodynamics of the quantum spin models. The classical lattice-gas model yields an excellent description of the quantum spin models up to quite large temperatures. The main peculiarity of the considered frustrated bilayer is a phase transition which occurs at low temperatures for a wide range of magnetic fields below the saturation magnetic field and belongs to the two-dimensional Ising model universality class.