Mott Glass and Criticality in a S=1/2 Bilayer Heisenberg Model with Interlayer Bond Dilution

Abstract

We employ the stochastic series expansion quantum Monte Carlo (SSE-QMC) method to investigate the $S=1/2$ antiferromagnetic Heisenberg model on a bilayer square lattice with diluted interlayer couplings. Both regular and random dilution patterns are considered. In systems with regular dilution, tuning the interlayer interaction drives a quantum phase transition from a Néel-ordered phase to a quantum disordered phase, consistent with the $O(3)$ universality class. In contrast, random dilution gives rise to a two-step transition: from the Néel phase to an intermediate Mott glass (MG) phase, followed by a transition to the quantum disordered phase. Within the MG phase, the uniform magnetic susceptibility exhibits a stretched-exponential temperature dependence ${\chi }_u\sim \exp (-b/T^{\alpha })$, $0<\alpha <1$. At the Néel-to-glass transition, quenched disorder modifies the critical exponents in a manner consistent with the Harris criterion. These findings provide new insights into disorder-driven quantum phase transitions and the emergence of glassy phases in diluted bilayer quantum magnets.