2012/03/10 by Sukhwinder Singh, Singh, Sukhwinder · 1 citation
Computer Science · Physics and Astronomy · #Computational Physics and Python Applications #Distributed and Parallel Computing Systems #FOS: Physical sciences #Quantum Physics (quant-ph) #Strongly Correlated Electrons (cond-mat.str-el) #cond-mat.str-el #quant-ph
paper · pdf · doi:10.48550/arxiv.1203.2222
PhD Thesis, 182 Pages. Chapters 2,3 and 4 incorporate previously published papers by the author. The material contained in chapters 5 and 6 describe the formalism for non-Abelian symmetries and has not been published elsewhere
openalex publication_date 2012/03/10 · arxiv created 2012/03/14 · arxiv updated 2012/03/16 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
In this thesis we extend the formalism of tensor network algorithms to incorporate global internal symmetries. We describe how to both numerically protect the symmetry and exploit it for computational gain in tensor network simulations. Our formalism is independent of the details of a specific tensor network decomposition since the symmetry constraints are imposed at the level of individual tensors. Moreover, the formalism can be applied to a wide spectrum of physical symmetries described by any discrete or continuous group that is compact and reducible. We describe in detail the implementation of the conservation of total particle number (U(1) symmetry) and of total angular momentum (SU(2) symmetry). Our formalism can also be readily generalized to incorporate more exotic symmetries such as conservation of total charge in anyonic systems.