English

Topological phases with generalized global symmetries

Strongly Correlated Electrons 2016-04-20 v2 High Energy Physics - Theory Quantum Physics

Abstract

We present simple lattice realizations of symmetry-protected topological (SPT) phases with qq-form global symmetries where charged excitations have qq spatial dimensions. Specifically, we construct dd space-dimensional models supported on a (d+1)(d+1)-colorable graph by using a family of unitary phase gates, known as multi-qubit control-ZZ 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.

Keywords

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)

R2 v1 2026-06-22T10:33:41.853Z