Higher-Order Entanglement and Many-Body Invariants for Higher-Order Topological Phases
Abstract
We discuss how strongly interacting higher-order symmetry protected topological (HOSPT) phases can be characterized from the entanglement perspective: First, we introduce a topological many-body invariant which reveals the non-commutative algebra between flux operator and rotations. We argue that this invariant denotes the angular momentum carried by the instanton which is closely related to the discrete Wen-Zee response and fractional corner charge. Second, we define a new entanglement property, dubbed `higher-order entanglement', to scrutinize and differentiate various higher-order topological phases from a hierarchical sequence of the entanglement structure. We support our claims by numerically studying a super-lattice Bose-Hubbard model that exhibits different HOSPT phases.
Keywords
Cite
@article{arxiv.2001.07724,
title = {Higher-Order Entanglement and Many-Body Invariants for Higher-Order Topological Phases},
author = {Yizhi You and Julian Bibo and Frank Pollmann},
journal= {arXiv preprint arXiv:2001.07724},
year = {2020}
}