Rapidly-converging methods for the location of quantum critical points from finite-size data

Details Rapidly-converging methods for the location of quantum critical points from finite-size data Rapidly-converging methods for the location of quantum critical points from finite-size data

2008-01-21

arxiv.org/abs/0801.3238v2

Phys. Rev. B 77, 155413 (2008)

Physics

Condensed Matter

Statistical Mechanics

9 pages, 2 EPS figures, RevTeX style. Updated to published version

Scientific paper

10.1103/PhysRevB.77.155413

We analyze in detail, beyond the usual scaling hypothesis, the finite-size convergence of static quantities toward the thermodynamic limit. In this way we are able to obtain sequences of pseudo-critical points which display a faster convergence rate as compared to currently used methods. The approaches are valid in any spatial dimension and for any value of the dynamic exponent. We demonstrate the effectiveness of our methods both analytically on the basis of the one dimensional XY model, and numerically considering c = 1 transitions occurring in non integrable spin models. In particular, we show that these general methods are able to locate precisely the onset of the Berezinskii-Kosterlitz-Thouless transition making only use of ground-state properties on relatively small systems.

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