System size scaling of topological defect creation in a second-order dynamical quantum phase transition

Details System size scaling of topological defect creation in a second-order dynamical quantum phase transition System size scaling of topological defect creation in a second-order dynamical quantum phase transition

2010-05-15

arxiv.org/abs/1005.2649v2

New J. Phys. 12: 095020,2010

Physics

Condensed Matter

Statistical Mechanics

20 pages of IOP style, 6 figures; as published in New Journal of Physics

Scientific paper

10.1088/1367-2630/12/9/095020

We investigate the system size scaling of the net defect number created by a rapid quench in a second-order quantum phase transition from an O(N) symmetric state to a phase of broken symmetry. Using a controlled mean-field expansion for large N, we find that the net defect number variance in convex volumina scales like the surface area of the sample for short-range correlations. This behaviour follows generally from spatial and internal symmetries. Conversely, if spatial isotropy is broken, e.g., by a lattice, and in addition long-range periodic correlations develop in the broken-symmetry phase, we get the rather counterintuitive result that the scaling strongly depends on the dimension being even or odd: For even dimensions, the net defect number variance scales like the surface area squared, with a prefactor oscillating with the system size, while for odd dimensions, it essentially vanishes.

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