Quantum Monte Carlo study of the transverse-field quantum Ising model on infinite-dimensional structures

Abstract

In a number of classical statistical-physical models, there exists a characteristic dimensionality called the upper critical dimension above which one observes the mean-field critical behavior. Instead of constructing high-dimensional lattices, however, one can also consider infinite-dimensional structures, and the question is whether this mean-field character extends to quantum-mechanical cases as well. We therefore investigate the transverse-field quantum Ising model on the globally coupled network and the Watts-Strogatz small-world network by means of quantum Monte Carlo simulations and the finite-size scaling analysis. We confirm that both the structures exhibit critical behavior consistent with the mean-field description. In particular, we show that the existing cumulant method has a difficulty in estimating the correct dynamic critical exponent and suggest that an order parameter based on the quantum-mechanical expectation value can be a practically useful numerical observable to determine critical behavior when there is no well-defined dimensionality.

13 pages, 18 figures

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Cited by in corpus (5)

• Quantum Monte Carlo Study of Long-Range Transverse-Field Ising Models on the Triangular Lattice
• Quantum critical behavior of the quantum Ising model on fractal lattices
• Quantum phase transition of the transverse-field quantum Ising model on scale-free networks
• Finite-size scaling analysis of the two-dimensional random transverse-field Ising ferromagnet
• Quantum magnetism on small-world networks