Definition and Classification of Fermi Surface Anomalies

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. 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.

Da-Chuan Lu is currently a Ph.D. candidate in condensed matter theory at UC San Diego, working with Prof. Yi-Zhuang You. He focuses on using quantum field theories to understand exotic quantum phases of matter and their transitions, such as deconfined quantum criticality and symmetric mass generation. He is also interested in applying the novel understanding to realistic condensed matter systems. He recently studied the loop group symmetry of the Fermi surface and its anomaly.

Faculty Hosts: Chao-Mian Jian, and Debanjan Chowdhury