Quantum Heisenberg antiferromagnet on low-dimensional frustrated lattices

TL;DR

This paper explores the low-temperature magnetization behavior of frustrated quantum Heisenberg antiferromagnets on two-leg ladder and bilayer lattices, revealing a connection to classical lattice gases and employing analytical and Monte Carlo methods.

Contribution

It introduces a lattice-gas description for these quantum models, enabling analytical and numerical analysis of their thermodynamic properties.

Findings

Analytical results for 1D systems showing the relation to classical lattice gases.

Monte Carlo simulations for 2D systems up to 100x100 sites.

Identification of a close relation between frustrated quantum antiferromagnets and classical models.

Abstract

Using a lattice-gas description of the low-energy degrees of freedom of the quantum Heisenberg antiferromagnet on the frustrated two-leg ladder and bilayer lattices we examine the magnetization process at low temperatures for these spin models. In both cases the emergent discrete degrees of freedom implicate a close relation of the frustrated quantum Heisenberg antiferromagnet to the classical lattice gas with finite nearest-neighbor repulsion or, equivalently, to the Ising antiferromagnet in a uniform magnetic field. Using this relation we obtain analytical results for thermodynamically large systems in the one-dimensional case. In the two-dimensional case we perform classical Monte Carlo simulations for systems of up to $100 \times 100$ sites.