A one-to-one correspondence is established between anomalous boundary SETs and critical states of internal versus crystalline fermionic SPT phases, including explicit mappings of time-reversal and mirror anomaly indicators.
That means two boundary phases with the same quantum anomaly could transfer into each other under by tuning some parameter of the surface Hamiltonian
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Correspondence of boundary theories between internal and crystalline symmetry protected topological phases
A one-to-one correspondence is established between anomalous boundary SETs and critical states of internal versus crystalline fermionic SPT phases, including explicit mappings of time-reversal and mirror anomaly indicators.