CMT/LTC Seminars

Symmetry protected topological spin systems on lattices in one and two dimensions and their classification

by Mr Michael Steinegger (ETHZ)




We study the classification of symmetry protected topological phases on quantum spin lattices in one and two dimensions. In one dimensional systems, we present how to define a topological in- dex with on-site symmetry using an operator algebraic approach. In two dimensions, we provide the proof of the 3-cocycle relation for the topological index. The abstract theory of Finitely correlated states and Valence bond states is thoroughly analyzed and further developed to derive covariance relations for on-site symmetries. The formalism and GNS construction of a newly-developed class of states is introduced. Finitely correlated states will arise as a variant thereof. We conclude by establishing the AKLT ground state as a Finitely correlated state. By explicit computation, we will demonstrate that the S = 1 AKLT and trivial model belong to distinguishable symmetry protected phases with respect to the Z2 × Z2 -symmetry.

Organized by

Laboratory for Theoretical and Computational Physics

Host: Prof. Christopher Mudry