Year-end Sale % OFF 
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 $C_n$ 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.
Highlights
A decade of intense effort has resulted in a thorough classification and characterization of symmetry protected topological phases of fermionic and bosonic systems [1,2,3,4,5,6,7]
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 noncommutative algebra between a flux operator and Cn rotations
We propose two complementary approaches to characterize different HOSPT phases: First, we introduce a many-body invariant that differentiates nontrivial HOSPT phases from trivial ones based on the fact that its U(1) instantons carry angular momentum, which implies that the U(1) flux insertion operator does not commute with the Cn rotation symmetry
Summary
A decade of intense effort has resulted in a thorough classification and characterization of symmetry protected topological phases of fermionic and bosonic systems [1,2,3,4,5,6,7]. We propose two complementary approaches to characterize different HOSPT phases: First, we introduce a many-body invariant that differentiates nontrivial HOSPT phases from trivial ones based on the fact that its U(1) instantons carry angular momentum, which implies that the U(1) flux insertion operator does not commute with the Cn rotation symmetry. This noncommutative algebra uniquely characterizes HOSPT phases with fractional charges at the corners. The entanglement of HOSPT phases manifests a branching structure, where any nondegenerate eigenvector of the initial entanglement spectrum contains a degenerate entanglement spectrum upon further cuts
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
