The superfluid to insulator quantum phase transition of a three-dimensional particle-hole symmetric system of disordered bosons is studied. To this end, a site-diluted quantum rotor Hamiltonian is mapped onto a classical (3+1)-dimensional XY model with columnar disorder and analyzed by means of large-scale Monte Carlo simulations. The superfluid-Mott insulator transition of the clean, undiluted system is in the four-dimensional XY universality class and shows mean-field critical behavior with logarithmic corrections. The clean correlation length exponent ν=1/2 violates the Harris criterion, indicating that disorder must be a relevant perturbation. For nonzero dilutions below the lattice percolation threshold of pc=0.688392, our simulations yield conventional power-law critical behavior with dilution-independent critical exponents z=1.67(6), ν=0.90(5), β/ν=1.09(3), and γ/ν=2.50(3). The critical behavior of the transition across the lattice percolation threshold is controlled by the classical percolation exponents. Our results are discussed in the context of a classification of disordered quantum phase transitions, as well as experiments in superfluids, superconductors, and magnetic systems.



Research Center/Lab(s)

Center for High Performance Computing Research


This work was supported in part by the NSF under Grants No. PHY-1125915 and No. DMR-1506152. T.V. acknowledges the hospitality of the Kavli Institute for Theoretical Physics, where part of the work was performed.

Keywords and Phrases

Quantum phase Transittras; Superfluidity; Quantum fluids and solids; Superconductors (materials); Insulators; Disordered superconductors

International Standard Serial Number (ISSN)

2469-9950; 2469-9969

Document Type

Article - Journal

Document Version

Final Version

File Type





© 2018 American Physical Society (APS), All rights reserved.

Publication Date

01 Aug 2018

Included in

Physics Commons