Pantheon SEMPARIS Le serveur des séminaires parisiens Paris

Status Confirmed
Seminar Series SEM-LPTMC
Subjects cond-mat
Date Thursday 16 January 2025
Time 14:00
Institute LPTMC
Seminar Room Jussieu, towers 13-12, 5th floor, room 5-23, LPTMC seminar room
Speaker's Last Name Wieder
Speaker's First Name Benjamin
Speaker's Email Address
Speaker's Institution IPhT Saclay
Title Monopole Quantum Numbers and Projective Representations in Stable and Fragile Topological Crystalline Insulators
Abstract Over the past 15 years, a dizzying array of noninteracting topological insulator (TI) and topological crystalline insulator (TCI) phases have been theoretically predicted and identified in real materials. While the TI states are well understood, the TCI states – which comprise the majority of topological materials in nature – exhibit more complicated classification groups and boundary states and carry more ambiguous response signatures. For earlier variants of interacting symmetry-protected topological states (SPTs), both the classification and response were clarified through the many-body quantum numbers of the 0D collective excitations bound to crystal and electromagnetic defects, such as magnetic fluxes and monopoles. In particular, when 0D defects exhibit fractionalized quantum numbers, or more generally projective representations of the local many-body symmetry group, this can indicate the presence of quantized responses in the bulk that are governed by long-wavelength topological field theories that are stable to symmetric interactions. In this talk, I will introduce numerical methods for computing defect quantum numbers in stable and fragile TCI states via the reduced density matrix, revealing a deep connection between defect quantum numbers and the entanglement spectrum. Surprisingly, we find that when crystal symmetries are included in the local symmetry group, defects can appear to transform projectively even in Wannierizable (fragile) insulators, casting doubt on the suitability of magnetic monopoles for characterizing the TCI states present in real 3D materials. Our results represent a crucial step towards describing TCIs beyond tight-binding models and frameworks like “higher- order topology,” and facilitate more direct connections between free-fermion TCIs and interacting SPTs.
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