Symmetry-resolved entanglement in symmetry-protected topological phases

  Daniel Azses [1,2]  ,  Eran Sela [3]  
[1] Department of Physics, Bar-Ilan University, Ramat Gan 5290002, Israel
[2] Center for Quantum Entanglement Science and Technology, Bar-Ilan University, Ramat Gan 5290002, Israel
[3] School of Physics and Astronomy, Tel Aviv University, Tel Aviv 6997801, Israel

Symmetry-protected topological phases (SPTs) have universal degeneracies in the entanglement spectrum in one dimension. Here we formulate this phenomenon in the framework of symmetry-resolved entanglement (SRE) using cohomology theory. We develop a general approach to compute entanglement measures of SPTs in any dimension and specifically SRE via a discrete path integral on multisheet Riemann surfaces with generalized defects. The resulting path integral is expressed in terms of group cocycles describing the topological actions of SPTs. Their cohomology classification allows us to identify universal entanglement properties. Specifically, we demonstrate an equiblock decomposition of the reduced density matrix into symmetry sectors, for all one-dimensional topological phases protected by finite Abelian unitary symmetries.