2010/05/31 by Michael Uhlmann, Ralf Schützhold, Uwe R. Fischer +1 · 32 citations
Physics and Astronomy · #Dimension (graph theory) #Isotropy #Phase (matter) #Phase transition #Quantum #Quantum many-body systems #Quantum phase transition #Scaling #Surface (topology) #Theoretical and Computational Physics #Topological Materials and Phenomena #cond-mat.stat-mech #gr-qc #quant-ph
paper · pdf · doi:10.1088/1367-2630/12/9/095020
published in New Journal of Physics 12(9), 095020 (IOP Publishing) · 20 pages of IOP style, 6 figures; as published in New Journal of Physics
arxiv created 2010/09/30 · openalex publication_date 2010/09/30 · arxiv updated 2015/03/16 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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 as 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 as the surface area squared, with a prefactor oscillating with the system size, while for odd dimensions, it essentially vanishes.