Mott glass phase in a diluted bilayer Heisenberg quantum antiferromagnet

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We use quantum Monte Carlo simulations to study a dimer-diluted S=1/2 Heisenberg model on a bilayer square lattice with intralayer interaction J₁ and interlayer interaction J₂. Below the classical percolation threshold pc, the system has three phases reachable by tuning the interaction ratio g=J₂/J₁: a Neel ordered phase, a gapless quantum glass phase, and a gapped quantum paramagnetic phase. We present the ground-state phase diagram in the plane of dilution p and interaction ratio g. The quantum glass phase is certified to be of the gapless Mott glass type, having a uniform susceptibility vanishing at zero temperature T and following a stretched exponential form at T>0; χᵤ (-b/Tα) with α< 1. At the phase transition point from Neel ordered to Mott glass, we find that the critical exponents are different from those of the clean system described by the standard O(3) universality class in 2+1 dimensions.