Open AccessTensor network approach to two-dimensional Yang–Mills theories
Author(s) -
Masafumi Fukuma,
Daisuke Kadoh,
Nobuyuki Matsumoto
Publication year - 2021
Publication title -
progress of theoretical and experimental physics
Language(s) - English
Resource type - Journals
ISSN - 2050-3911
DOI - 10.1093/ptep/ptab143
Subject(s) - tensor (intrinsic definition) , physics , character (mathematics) , stress–energy tensor , mathematical physics , tensor contraction , tensor density , group (periodic table) , gauge group , representation (politics) , tensor field , gauge theory , pure mathematics , exact solutions in general relativity , mathematics , quantum mechanics , geometry , politics , political science , law
We propose a novel tensor network representation for two-dimensional Yang–Mills theories with arbitrary compact gauge groups. In this method, tensor indices are given directly by group elements with no direct use of the character expansion. We apply the tensor renormalization group method to this tensor network for SU(2) and SU(3), and find that the free energy density and the energy density are accurately evaluated. We also show that the singular value decomposition of a tensor has a group-theoretic structure and can be associated with the character expansion.