Fractionalization as an alternate to charge ordering in electronic insulators

TL;DR

This paper investigates the possibility of insulating quantum phases at partial lattice filling that preserve lattice symmetry, characterized by fractionalized excitations and topological order, challenging traditional charge ordering concepts.

Contribution

It introduces the concept of Quantum Charge Liquids (QCL) as an alternative to charge ordering, establishing constraints on their topological order and analyzing minimal ground state degeneracies.

Findings

Fermionic QCLs at rational fillings have a minimal ground state degeneracy of 4q^2 on a torus.

Fermionic QCLs exhibit larger degeneracy than bosonic counterparts at the same filling.

The paper discusses physical systems that could host fermionic QCL phases.

Abstract

Incompressible insulating phases of electronic systems at partial filling of a lattice are often associated with charge ordering that breaks lattice symmetry. The resulting phases have an enlarged unit cell with an effective integer filling. Here we explore the possibility of insulating states - which we dub "Quantum Charge Liquids" (QCL) - at partial lattice filling that preserve lattice translation symmetry. Such QCL phases must necessarily either have gapped fractionally charged excitations and associated topological order or have gapless neutral excitations. We establish some general constraints on gapped fermionic QCL phases that restrict the nature of their topological order. We prove a number of results on the minimal topological order that is consistent with the lattice filling. In particular we show that at rational fillings $\nu = p/q$ with $q$ an even integer the minimal ground state degeneracy on a torus of the fermionic QCL is $4q^2$, 4 times larger than that of the bosonic QCL at the same filling. We comment on models and physical systems which may host fermionic QCL phases and discuss the phenomenology of these phases.