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

Abstract

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 due to the limited range of applicability of the finite-size scaling form. By quantum Monte Carlo simulation, it is shown that the same holds in the case of N=1.

18 pages, 4 figures

References in corpus (3)

• Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms
• Finite size scaling of the correlation length above the upper critical dimension
• Universal Scaling of the Conductivity at the Superfluid-Insulator Phase Transition

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