Featureless and non-fractionalized Mott insulators on the honeycomb lattice at 1/2 site filling

TL;DR

This paper constructs and demonstrates the existence of featureless Mott insulators on the honeycomb lattice at half filling, showing that lack of order does not necessarily imply fractionalization even when free particles are metallic.

Contribution

It provides explicit wave functions for bosons and electrons at half filling on the honeycomb lattice, proving the possibility of featureless Mott insulators in this setting.

Findings

Featureless Mott insulators exist at half filling on the honeycomb lattice.

Lack of order at zero temperature does not imply fractionalization.

Construction generalizes to symmorphic lattices at integer fillings in any dimension.

Abstract

Within the Landau paradigm, phases of matter are distinguished by spontaneous symmetry breaking. Implicit here is the assumption that a completely symmetric state exists: a paramagnet. At zero temperature such quantum featureless insulators may be forbidden, triggering either conventional order or topological order with fractionalized excitations. Such is the case for interacting particles when the particle number per unit cell, f, is not an integer. But, can lattice symmetries forbid featureless insulators even at integer f? An especially relevant case is the honeycomb (graphene) lattice --- where free spinless fermions at f=1 (the two sites per unit cell mean f=1 is half filling per site) are always metallic. Here we present wave functions for bosons, and a related spin-singlet wave function for spinful electrons, on the f=1 honeycomb, and demonstrate via quantum to classical mappings that they do form featureless Mott insulators. The construction generalizes to symmorphic lattices at integer f in any dimension. Our results explicitly demonstrate that in this case, despite the absence of a non-interacting insulator at the same filling, lack of order at zero temperature does not imply fractionalization.