Topological phases with generalized global symmetries
Abstract
We present simple lattice realizations of symmetry-protected topological (SPT) phases with -form global symmetries where charged excitations have spatial dimensions. Specifically, we construct space-dimensional models supported on a -colorable graph by using a family of unitary phase gates, known as multi-qubit control- gates in quantum information community. In our construction, charged excitations of different dimensionality may coexist and form a short-range entangled state which is protected by symmetry operators of different dimensionality. Non-triviality of proposed models, in a sense of quantum circuit complexity, is confirmed by studying protected boundary modes, gauged models and corresponding gapped domain walls. We also comment on applications of our construction to quantum error-correcting codes, and discuss corresponding fault-tolerant logical gates.
Cite
@article{arxiv.1508.03468,
title = {Topological phases with generalized global symmetries},
author = {Beni Yoshida},
journal= {arXiv preprint arXiv:1508.03468},
year = {2016}
}
Comments
32 pages, 17 figures, single column (v2, corrected minor mistakes and typos, to appear in PRB)