Braiding properties of worldline configurations in hardcore lattice bosons

Abstract

In this manuscript, we study braiding properties of worldline configurations for a variety of ground-states of hardcore Bose-Hubbard models in two dimensions. Configurations are collections of particle paths and result from the path-integral formulation of statistical mechanics. For hard-core bosons, configurations can be seen as geometric braids and therefore can be assigned a certain topological structure, i.e. a way to classify braiding events among worldlines. By means of Monte Carlo calculations, we study superfluid phase and a variety of insulating phases and observe that ground-states of different quantum phases correspond to different probability distributions of braiding properties.

arXiv comment11 pages, 5 figures. The current version focuses on the discussion of braiding properties of worldline configurations. The study of phase transitions and permutation cycles has been moved to a new manuscript: arXiv:1912.00080. The current manuscript has been accepted for publication on Scientific Reports

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