Classification and construction of higher-order symmetry protected topological phases of interacting bosons

Alex Rasmussen; Yuan-Ming Lu

Classification and construction of higher-order symmetry protected topological phases of interacting bosons

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arxiv 1809.07325 v2 pith:QF2SK443 submitted 2018-09-19 cond-mat.str-el

Alex Rasmussen , Yuan-Ming Lu This is my paper · ORCID

classification cond-mat.str-el

keywords phaseshosptsymmetrytopologicaldimensionshigher-orderprotectedbosons

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Motivated by the recent discovery of higher-order topological insulators, we study their counterparts in strongly interacting bosons: `higher-order symmetry protected topological (HOSPT) phases'. While the usual (1st-order) SPT phases in d spatial dimensions support anomalous (d-1)-dimensional surface states, HOSPT phases in d dimensions are characterized by topological boundary states of dimension (d-2) or smaller, protected by certain global symmetries and robust against disorders. Based on a dimensional reduction analysis, we show that HOSPT phases can be built from lower-dimensional SPT phases in a way that preserves the associated crystalline symmetries. When the total symmetry is a direct product of global and crystalline symmetry groups, we are able to classify the HOSPT phases using the K\"unneth formula of group cohomology. Based on a decorated domain wall picture of the K\"unneth formula, we show how to systematically construct the HOSPT phases, and demonstrate our construction with many examples in two and three dimensions.

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Higher-order topological phase without crystalline symmetry
cond-mat.str-el 2019-08 conditional novelty 7.0 of 10

Subsystem symmetries can protect gapless hinges and corners in interacting 3D models, yielding higher-order topological phases that require no crystalline symmetry.

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