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 —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 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 and consistent with 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 and exponents maintain values consistent with those of the percolation transition. These results contradict the conventional scaling, which predicts ; and they suggest a possible relationship between the SF-BG transition and percolation of phase coherence.
- Received 24 November 2022
- Revised 17 December 2023
- Accepted 18 December 2023
DOI:https://doi.org/10.1103/PhysRevB.109.L020405
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