Symmetry protected Berry phases and edge states with interaction

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Although absence of the local order parameters is a fundamental feature of the topological phases, the Berry connection that represents a quantum interference of many body states successfully characterizes the bulk of the topological phases. The Chern number for the bulk of the quantum Hall states is a typical example. Also, with boundaries, appearance of local modes as the edge states characterizes the phase as the bulk-edge correspondence. As for the short range entangled state, the Berry phase that is quantized due to symmetry is used as a “quantum” local order parameter of the bulk. Z_2 Berry phase for the Haldane phase of the spin 1 quantum spin chain is a typical example. Here again, with boundaries, low energy local modes as the edge states appear associated with the nontrivial Berry phases as the bulk-edge correspondence. Focusing on the systems with interaction, we demonstrate the use of the symmetry protected Berry phases and the bulk-edge correspondence for various examples such as the generic valence bond solid (VBS) states and the corner states of the higher order topological phases.

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• Standort: Hannover TIB
• Umfang: 129MB, 00:36:42:08 (unknown)
• Sprache: Englisch
• Anmerkungen: Audiovisuelles Material

Verweise und Beziehungen

• Erschienen in: Topological Phases of Interacting Quantum Systems (19w5034) ; (Jan. 2019)

Beteiligte, Orts- und Zeitangaben

• Ereignis: Veröffentlichung
• (wer): Banff International Research Station (BIRS) for Mathematical Innovation and Discovery
• (wann): 2019-01-01
• Beteiligte Personen und Organisationen: Hatsugai, Yasuhiro ; Schulz-Baldes, Hermann (Organization) ; Prodan, Emil (Organization) ; Villegas-Blas, Carlos (Organization)

Weitere Informationen

• DOI: 10.5446/56091