Towards a microscopic model for an electronic quantum charge liquid

• URL: http://arxiv.org/abs/2604.25992v1
• Date: Tue, 28 Apr 2026 18:00:00 GMT
• Title: Towards a microscopic model for an electronic quantum charge liquid
• Abstract summary: 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.<n>The gapped nature of this state, along with its $mathbbZ_4$ symmetry, leads us to propose that it is an example of the elusive bosonic QCL displaying the minimal $mathbbZ_4$ topological order.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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 $ν=3/2$ we pair them to get bosons at filling $ν=3/4$ 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 $ν= 3/4$. 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.

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