Finite-size scaling for quantum criticality above the upper critical dimension: Superfluid-Mott-insulator transition in three dimensions.
The validity of modified finite-size scaling above the upper critical dimension is demonstrated for the quantum phase transition whose dynamical critical exponent is z=2. We consider the N -component Bose-Hubbard model, which is exactly solvable and exhibits mean-field type critical phenomena in the large- N limit. The modified finite-size scaling holds exactly in that limit. However, the usual procedure, taking the large system-size limit with fixed temperature, does not lead to the expected (and correct) mean-field critical behavior because of the limited range of applicability of the finite-size scaling form. By quantum Monte Carlo simulation, it is shown that the modified finite-size scaling holds in the case of N=1.
Kato
Yasuyuki
Y
Institute for Solid State Physics, University of Tokyo, Kashiwa, Chiba 277-8581, Japan. katoyasu@issp.u-tokyo.ac.jp
Kawashima
Naoki
N