Bond-Dilution-Induced Quantum Phase Transitions in Heisenberg Antiferromagnets

TL;DR

This study uses quantum Monte Carlo simulations to explore how bond dilution affects the ground state of a square-lattice antiferromagnetic Heisenberg model, revealing phase transitions from disordered to ordered states depending on dilution strength.

Contribution

It demonstrates the different effects of bond versus site dilution on magnetic order, highlighting the emergence of long-range order at finite bond dilution thresholds.

Findings

Weak bond dilution induces a disordered state with a mid gap.

Stronger bond dilution leads to antiferromagnetic long-range order.

Finite critical concentration is required for bond dilution-induced order.

Abstract

Bond-dilution effects on the ground state of the square-lattice antiferromagnetic Heisenberg model, consisting of coupled bond-alternating chains, are investigated by means of the quantum Monte Carlo simulation. It is found that, when the ground state of the non-diluted system is a non-magnetic state with a finite spin gap, a sufficiently weak bond dilution induces a disordered state with a mid gap in the original spin gap, and under a further stronger bond dilution an antiferromagnetic long-range order emerges. While the site-dilution-induced long-range order is induced by an infinitesimal concentration of dilution, there exists a finite critical concentration in the case of bond dilution. We argue that this essential difference is due to the occurrence of two types of effective interactions between induced magnetic moments in the case of bond dilution, and that the antiferromagnetic long-range-ordered phase does not appear until the magnitudes of the two interactions become comparable.