Low-energy properties of anisotropic two-dimensional spin-1/2 Heisenberg models in staggered magnetic fields

TL;DR

This study investigates the low-energy properties and phase transitions of anisotropic 2D spin-1/2 Heisenberg models under staggered magnetic fields, revealing how fields induce gaps and phase changes, with implications for quasi-1D to 2D crossover.

Contribution

It provides a comprehensive phase diagram and scaling analysis of the 2D anisotropic Heisenberg model in staggered fields using Monte Carlo simulations, highlighting the quantum phase transition and crossover phenomena.

Findings

Energy gap opens immediately with commensurate fields following a power law.

Quantum phase transition from gapless to gapped phases occurs under competing fields.

Quasi-1D behavior persists around the quantum critical point.

Abstract

We present a systematic study of the anisotropic spin-1/2 Heisenberg model in staggered magnetic fields in two dimensions (2D). To mimic real materials, we consider a system of coupled, antiferromagnetic chains, whose interchain interaction can be either ferro- or antiferromagnetic. When the staggered field is commensurate with the magnetic interactions, an energy gap opens immediately and follows a power law as a function of the applied field, similar to the situation in 1D. When the field competes with the interactions, a quantum phase transition (QPT) occurs from a gapless, magnetically ordered phase at low fields to a gapped, disordered regime. We use a continuous-time Monte Carlo method to compute the staggered moment of the ordered phases and the spin gap of the disordered phases. We deduce the phase diagrams as functions of the anisotropy ratio and the applied field, and calculate the scaling behavior of the models in both quantities. We show that in the competitive case, the staggered field acts to maintain a regime of quasi-1D behavior around the QPT, and we discuss as a consequence the nature of the crossover from 1D to 2D physics.