Bound states of three fermions forming symmetry-protected topological phases

TL;DR

This paper introduces a theoretical framework for constructing symmetry-protected topological phases using bound states of three fermions, called clustons, which are distinct from free fermion states and can be realized in cold atom systems.

Contribution

It presents a simple construction of fermionic SPT phases via three-fermion bound states and links them to free fermion and bosonic SPT states, offering new insights and methods.

Findings

Cluston-based topological phases are distinct from free fermion states.

These phases can be realized in cold atom systems.

New bosonic parton constructions of SPT phases are proposed.

Abstract

We propose a simple theoretical construction of certain short-range entangled phases of interacting fermions, by putting the bound states of three fermions (which we refer to as clustons) into topological bands. We give examples in two and three dimensions, and show that they are distinct from any free fermion state. We further argue that these states can be viewed as combinations of certain free fermion topological states and bosonic symmetry-protected topological (SPT) states. This provides a conceptually simple understanding of various SPT phases, and the possibility of realizing them in cold atom systems. New parton constructions of these SPT phases in purely bosonic systems are proposed. We also discuss a related anomaly in two dimensional Dirac theories, which is the gravitational analogue of the parity anomaly.