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

Research output: Contribution to journalArticle

16 Citations (Scopus)

Abstract

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
Volume85
Issue number1
DOIs
Publication statusPublished - 2012 Jan 17

Fingerprint

Phase transitions
scaling
Dimerization
Anisotropy
simulation
Stiffness
indication
dimerization
boxes
Monte Carlo simulation
stiffness
exponents
anisotropy
Direction compound

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics

Cite this

@article{7a46c0ca1e164b4caa18ca045fc8694b,
title = "Monte Carlo simulations of an unconventional phase transition for a two-dimensional dimerized quantum Heisenberg model",
abstract = "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.",
author = "Jiang, {F. -J.}",
year = "2012",
month = "1",
day = "17",
doi = "10.1103/PhysRevB.85.014414",
language = "English",
volume = "85",
journal = "Physical Review B",
issn = "2469-9950",
publisher = "American Physical Society",
number = "1",

}

TY - JOUR

T1 - Monte Carlo simulations of an unconventional phase transition for a two-dimensional dimerized quantum Heisenberg model

AU - Jiang, F. -J.

PY - 2012/1/17

Y1 - 2012/1/17

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84856427150&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84856427150&partnerID=8YFLogxK

U2 - 10.1103/PhysRevB.85.014414

DO - 10.1103/PhysRevB.85.014414

M3 - Article

VL - 85

JO - Physical Review B

JF - Physical Review B

SN - 2469-9950

IS - 1

M1 - 014414

ER -