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We study topological properties of 3D lattice dimer model. We demonstrate, that the dimer model on a bipartite lattice possesses topological defects, which are exactly characterized by Hopf invariant. We derive its explicit algebraic expression in terms of effective magnetic field of a dimer configuration. Thus, we solve the problem of topological classification of possible states in 3D lattice dimer model. In addition, we address the same problem using neural networks and obtain that on a non-bipartite lattice, dimer configurations are characterized by a Z2 topological invariant.
Education
Physics Department, Moscow State University, started Sept 2006, finished Feb 2012 - undergraduate degree.
Physics and Astronomy Department, McMaster University, started Sept 2012, finished May 2014 - M.Sc.
Physics and Astronomy Department, University ofWaterloo, started September 2014, finished August 2018 - PhD
Current position
Physics and Astronomy Department, University of California Santa Cruz, started October 2018, planning to finish October 2020 -postdoctoral scholar
Video Link（Jaccount needed）
https://vshare.sjtu.edu.cn/play/426cec0aef098f336facb5f342362c09