Quantum-critical scaling at the Bose-glass transition of the 3d diluted Heisenberg antiferromagnet in a field

TL;DR

This study investigates the quantum-critical scaling behavior at the Bose-glass transition in a disordered 3D Heisenberg antiferromagnet, revealing deviations from conventional scaling and a connection to percolation phenomena.

Contribution

It demonstrates that the SF-BG transition in a diluted Heisenberg antiferromagnet exhibits critical exponents consistent with percolation, challenging traditional scaling predictions.

Findings

Exponents match 3D percolation values.

Transition decouples from geometric percolation under magnetic field.

Contradicts the conventional scaling law $\\phi \geq 2$.

Abstract

The nature of the superfluid-to-Bose-glass (SF-BG) quantum phase transition, occurring in systems of interacting bosons immersed in a disordered environment, remains elusive. One fundamental open question is whether or not the transition obeys conventional scaling at quantum critical points (QCPs): this scaling would lock the value of the crossover exponent $\phi$ -- dictating the vanishing of the superfluid critical temperature upon approaching the QCP -- to the value of quantum critical exponents for the ground-state transition. Yet such a relation between exponents has been called into question by several numerical as well as experimental results on the SF-BG transition. Here we revisit this issue in the case of the $S=1/2$ Heisenberg antiferromagnet on a site-diluted cubic lattice, which lends itself to efficient quantum Monte Carlo simulations. Our results show that the model exhibits a percolation transition in zero applied field, with the correlation length exponent $\nu = 0.87(8)$ and $\phi = 1.1(1)$ consistent with 3d percolation. When applying a sufficiently strong magnetic field, the dilution-induced transition decouples from geometric percolation, and it becomes a SF-BG transition; nonetheless, the $\nu$ and $\phi$ exponents maintain values consistent with those of the percolation transition. These results contradict the conventional scaling, which predicts $\phi\geqslant 2$; and they suggest a close connection between the SF-BG transition and percolation.