Towards a microscopic model for an electronic quantum charge liquid

TL;DR

This paper proposes a microscopic model for an electronic quantum charge liquid (QCL) on a square lattice, demonstrating a gapped state with minimal $ ext{Z}_4$ topological order and discussing potential extensions.

Contribution

It introduces a tetramer bosonic model at filling $ u=3/4$ as a candidate for a $ ext{Z}_4$ topologically ordered QCL, supported by numerical evidence of a gapped phase.

Findings

The tetramer model exhibits a local $ ext{Z}_4$ symmetry.

Numerical studies show at least one gapped state with $ ext{Z}_4$ topological order.

The gapped state is distinguished by its symmetry and topological properties.

Abstract

We provide a route to constructing an electronic quantum charge liquid (QCL), a state made up of fermions at fractional filling of a lattice that does not break translation. Starting with spinless fermions at filling $\nu=3/2$ we pair them to get bosons at filling $\nu=3/4$ per unit cell. The tetramer model, a generalization of the dimer model, on the square lattice is evaluated as a candidate bosonic QCL at filling $\nu = 3/4$. It is shown that these models exhibit a local $\mathbb{Z}_4$ symmetry. Upon numerical study of a family of tetramer wavefunctions it is found that while one is gapless due to $\mathrm{U}(1)^3$ symmetry at least one other can be definitively shown to be gapped. The gapped nature of this state, along with its $\mathbb{Z}_4$ symmetry, leads us to propose that it is an example of the elusive bosonic QCL displaying the minimal $\mathbb{Z}_4$ topological order. We conclude by discussing possible extensions to other lattice geometries, electronic QCLs, and to Rydberg atoms.