Definition and Classification of Fermi Surface Anomalies
- URL: http://arxiv.org/abs/2302.12731v2
- Date: Fri, 7 Apr 2023 21:24:58 GMT
- Title: Definition and Classification of Fermi Surface Anomalies
- Authors: Da-Chuan Lu, Juven Wang, Yi-Zhuang You
- Abstract summary: We show that the gapless fermions on the Fermi surface can be viewed as the topological boundary modes of Chern insulators in the phase space.
We show that the momentum space dimensions should be counted as negative dimensions for SPT classification purposes.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: We propose that the Fermi surface anomaly of symmetry group $G$ in any
dimension is universally classified by $G$-symmetric interacting fermionic
symmetry-protected topological (SPT) phases in $(0+1)$-dimensional spacetime.
The argument is based on the perspective that the gapless fermions on the Fermi
surface can be viewed as the topological boundary modes of Chern insulators in
the phase space (position-momentum space). Given the non-commutative nature of
the phase space coordinates, we show that the momentum space dimensions should
be counted as negative dimensions for SPT classification purposes. Therefore,
the classification of phase-space Chern insulators (or, more generally
fermionic SPT phases) always reduces to a $(0+1)$-dimensional problem, which
can then be answered by the cobordism approach. In addition to the
codimension-1 Fermi surface case, we also discuss the codimension-$p$ Fermi
surface case briefly. We provide concrete examples to demonstrate the validity
of our classification scheme, and make connections to the recent development of
Fermi surface symmetric mass generation.
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