Critical Exponents of the Superfluid-Bose Glass Transition in Three-Dimensions

Abstract

Recent experimental and numerical studies of the critical-temperature exponent $\varphi$ for the superfluid-Bose glass universality in three-dimensional systems report strong violations of the key quantum critical relation, $\varphi =\nu z$, where $z$ and $\nu$ are the dynamic and correlation length exponents, respectively, and question the fundamental concepts underlying quantum critical phenomena. Using Monte Carlo simulations of the disordered Bose-Hubbard model, we demonstrate that previous work on the superfluid-to-normal fluid transition-temperature dependence on chemical potential (or magnetic field, in spin systems), $T_c\propto (\mu -{\mu }_c{)}^{\varphi }$, was misinterpreting transient behavior on approach to the fluctuation region with the genuine critical law. When the model parameters are modified to have a broad quantum critical region, simulations of both quantum and classical models reveal that the $\varphi =\nu z$ law [with $\varphi =2.7(2)$, $z=3$, and $\nu =0.88(5)$] holds true, resolving the $\varphi$-exponent "crisis".

5 pages, 6 figures

References in corpus (1)

• Criticality in a disordered quantum antiferromagnet by neutron diffraction

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