Investigation of a universal behavior between Néel temperature and staggered magnetization density for a three-dimensional quantum antiferromagnet
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We simulate the three-dimensional quantum Heisenberg model with a spatially anisotropic ladder pattern using the first principles Monte Carlo method. Our motivation is to investigate quantitatively the newly established universal relation T N /√c 3 ∝ ℳ s near the quantum critical point (QCP) associated with dimerization. Here T N , c, and ℳ s are the Néel temperature, the spinwave velocity, and the staggered magnetization density, respectively. For all the physical quantities considered here, such as T N and ℳ s , our Monte Carlo results agree nicely with the corresponding results determined by the series expansion method. In addition, we find it is likely that the effect of a logarithmic correction, which should be present in (3 + 1)-dimensions, to the relation T N /√c 3 ∝ ℳ s near the investigated QCP only sets in significantly in the region with strong spatial anisotropy.
KeywordsSolid State and Materials