Irrational charge from topological order

TL;DR

This paper demonstrates that topological order can be exploited to create Hamiltonians where quasiparticles have irrational intrinsic charges, contrasting with their quantized gauge charges, across various models.

Contribution

It introduces a method to generate Hamiltonians with quasiparticles possessing irrational intrinsic charges in topologically ordered systems.

Findings

Quasiparticles can have irrational intrinsic charges.

Gauge charges remain quantized despite irrational intrinsic charges.

Applicable to multiple topologically ordered models.

Abstract

Topological or deconfined phases of matter exhibit emergent gauge fields and quasiparticles that carry a corresponding gauge charge. In systems with an intrinsic conserved U(1) charge, such as all electronic systems where the Coulombic charge plays this role, these quasiparticles are also characterized by their intrinsic charge. We show that one can take advantage of the topological order fairly generally to produce periodic Hamiltonians which endow the quasiparticles with continuously variable, generically irrational, intrinsic charges. Examples include various topologically ordered lattice models, the three dimensional RVB liquid on bipartite lattices as well as water and spin ice. By contrast, the gauge charges of the quasiparticles retain their quantized values.