Finite-Size Scaling for Quantum Criticality above the Upper Critical Dimension: Superfluid-Mott-Insulator Transition in Three Dimensions

摘要

Validity of modified finite-size scaling above the upper critical dimensionis demonstrated for the quantum phase transition whose dynamical criticalexponent is $z=2$. We consider the $N$-component Bose-Hubbard model, which isexactly solvable and exhibits mean-field type critical phenomena in thelarge-$N$ limit. The modified finite-size scaling holds exactly in that limit.However, the usual procedure, taking the large system-size limit with fixedtemperature, does not lead to the expected (and correct) mean-field criticalbehavior due to the limited range of applicability of the finite-size scalingform. By quantum Monte Carlo simulation, it is shown that the same holds in thecase of N=1.