Quantum Monte Carlo study of the transverse-field quantum Ising modelon infinite-dimensional structures
2011 (English)In: Physical Review B Condensed Matter, ISSN 0163-1829, E-ISSN 1095-3795, Vol. 84, 174419- p.Article in journal (Refereed) Published
In a number of classical statistical-physical models, there exists acharacteristic dimensionality called the upper critical dimension abovewhich one observes the mean-field critical behavior. Instead of constructinghigh-dimensional lattices, however, one can also considerinfinite-dimensional structures, and the question is whether this mean-fieldcharacter extends to quantum-mechanical cases as well. We thereforeinvestigate the transverse-field quantum Ising model on the globally couplednetwork and on the Watts-Strogatz small-world network by means of quantum MonteCarlo simulations and the finite-size scaling analysis. We confirm that bothof the structures exhibit critical behavior consistent with the mean-fielddescription. In particular, we show that the existing cumulant methodhas difficulty in estimating the correct dynamic critical exponent andsuggest that an order parameter based on the quantum-mechanicalexpectation value can be a practically useful numerical observable todetermine critical behavior when there is no well-defined dimensionality.
Place, publisher, year, edition, pages
American Physical Society , 2011. Vol. 84, 174419- p.
Condensed Matter Physics
IdentifiersURN: urn:nbn:se:umu:diva-50288DOI: 10.1103/PhysRevB.84.174419OAI: oai:DiVA.org:umu-50288DiVA: diva2:461356