Filling constraints on fermionic topological order in zero magnetic field

TL;DR

This paper investigates the constraints on fermionic topological order in two-dimensional electron systems at fractional filling and zero magnetic field, revealing differences from bosonic systems, especially at even denominator fillings.

Contribution

It demonstrates that fermionic systems have distinct topological orders under Lieb-Schultz-Mattis constraints, especially highlighting differences at even and odd denominator fillings.

Findings

Fermionic topological orders differ from bosonic ones under microscopic constraints.

Even denominator fillings show stronger deviation from bosonic cases.

Some results extend to three-dimensional systems.

Abstract

We consider two-dimensional electron systems in zero magnetic field at fractional filling. For such systems a Lieb-Schultz-Mattis theorem applies, forbidding the existence of a trivial insulator. However, the theorem does not distinguish between bosonic and fermionic systems. In this work we argue that in the case of fermionic systems, the topological orders that are compatible with the microscopic constraints are in general different from the bosonic case. We find different results in the cases of even and odd denominator fillings, with even denominator fillings deviating stronger from the bosonic case. Part of our results also hold in three dimensions.