Crystalline equivalent boundary-bulk correspondence of two-dimensional topological phases - INSPIRE

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Crystalline equivalent boundary-bulk correspondence of two-dimensional topological phases

Dec 29, 2021

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2112.14567 [cond-mat.str-el]

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Abstract: (arXiv)

The boundary of topological phases of matter can manifest its topology nature, which leads to the so-called boundary-bulk correspondence (BBC) of topological phases. In this Letter, we construct a one-to-one correspondence between the boundary theories of fermionic SPT (fSPT) phases protected by crystalline symmetry and on-site symmetry in 2D fermionic systems, which follow the so-called crystalline equivalence principle. We dub such correspondence crystalline equivalent BBC. We illustrate this correspondence by two simple examples and as an application, we discover the topological boundary theory of 2D fSPT phase with spin-1/2 fermions, protected by a non-Abelian group

\mathbb{Z}_4\rtimes\mathbb{Z}_2^T

with

A^4=\mathcal{T}^2=P_f

where

A

is the generator of

\mathbb{Z}_4

, from its crystalline equivalent partner -- 2D higher-order fSPT phase with spinless fermions, protected by

D_4

symmetry.

Note:

4+epsilon pages, 3 figures, with supplementary materials. Comments are welcome

phase: topological
fermion: spinless
group: nonabelian
dimension: 2
crystal
equivalence principle
topology
boundary condition
Z(4)

References(79)

Figures(0)

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