Phase Structure of 1d Interacting Floquet Systems I: Abelian SPTs

• Published in: arXiv.org
• Main Authors: von Keyserlingk, C W, Sondhi, S L
• Format: Paper Journal Article
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 15.07.2016
• Subjects: Classification; Hamiltonian functions; Physics - Disordered Systems and Neural Networks; Physics - Strongly Correlated Electrons; Solid phases; Symmetry
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.1602.02157

Recent work suggests that a sharp definition of `phase of matter' can be given for some quantum systems out of equilibrium---first for many-body localized systems with time independent Hamiltonians and more recently for periodically driven or Floquet localized systems. In this work we propose a classification of the finite abelian symmetry protected phases of interacting Floquet localized systems in one dimension. We find that the different Floquet phases correspond to elements of \(\text{Cl}\times\mathcal{A}_G\), where \(\text{Cl}\) is the undriven interacting classification, and \(\mathcal{A}_G\) is a set of (twisted) 1d representations of \(G\). We will address symmetry broken phases in a subsequent paper.