Monte Carlo simulations of an unconventional phase transition for a two-dimensional dimerized quantum Heisenberg model

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Motivated by the indication of a new critical theory for the spin-1/2 Heisenberg model with a spatially staggered anisotropy on the square lattice, we reinvestigate the phase transition of this model induced by dimerization using first-principle Monte Carlo simulations. We focus on studying the finite-size scaling of ρ s12L and ρ s22L, where L stands for the spatial box size used in the simulations and ρ si, with i{1,2}, is the spin-stiffness in the i-direction. Remarkably, while we observe a large correction to scaling for the observable ρ s12L, the data for ρ s22L exhibit a good scaling behavior without any indication of a large correction. As a consequence, we are able to obtain a numerical value for the critical exponent ν, which is consistent with the known O(3) result with moderate computational effort. Further, we additionally carry out an unconventional finite-size scaling analysis with which we assume that the ratio of the spatial winding numbers squared is fixed through all simulations. The theoretical correctness of our idea is argued and its validity is confirmed. Using this unconventional finite-size scaling method, even from ρ s1L, which receives the most serious correction among the observables considered in this study, we are able to arrive at a value for ν consistent with the expected O(3) value. A detailed investigation to compare these two finite-size scaling methods should be performed.

Original languageEnglish
Article number014414
JournalPhysical Review B - Condensed Matter and Materials Physics
Issue number1
Publication statusPublished - 2012 Jan 17


ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics

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