Construction and classification of point group symmetry protected topological phases in 2D interacting fermionic systems

TL;DR

This paper systematically constructs and classifies point group symmetry-protected topological phases in 2D interacting fermionic systems, discovering new states unique to interactions and verifying the crystalline equivalence principle.

Contribution

It extends the classification scheme of SPT phases to 2D interacting fermions, introducing novel fermionic SPT states and confirming the crystalline equivalence principle.

Findings

Discovery of fermionic SPT states exclusive to interactions

Verification of the crystalline equivalence principle in 2D fermionic systems

Potential for experimental realization in 2D correlated superconductors

Abstract

The construction and classification of symmetry-protected topological (SPT) phases in interacting bosonic and fermionic systems have been intensively studied in the past few years. Very recently, a complete classification and construction of space group SPT phases were also proposed for interacting bosonic systems. In this paper, we attempt to generalize this classification and construction scheme systematically into interacting fermion systems. In particular, we construct and classify point group SPT phases for 2D interacting fermion systems via lower-dimensional block-state decorations. We discover several intriguing fermionic SPT states that can only be realized in interacting fermion systems (i.e., not in free-fermion or bosonic SPT systems). Moreover, we also verify the recently conjectured crystalline equivalence principle for 2D interacting fermion systems. Finally, the potential experimental realization of these new classes of point group SPT phases in 2D correlated superconductors is addressed.