Bosonic Pfaffian State in the Hofstadter-Bose-Hubbard Model

TL;DR

This paper demonstrates that a non-Abelian Pfaffian state can be realized in a Hofstadter-Bose-Hubbard model using cold atoms, showing potential for experimental observation of exotic topological quantum states.

Contribution

It provides the first evidence of a lattice analog of the non-Abelian Pfaffian state in the Hofstadter-Bose-Hubbard model at filling factor one.

Findings

Identification of a lattice Pfaffian state at flux /6

Observation of an incompressible charge gap

Evidence of paired correlations and related density wave phenomena

Abstract

Topological states of matter, such as fractional quantum Hall states, are an active field of research due to their exotic excitations. In particular, ultracold atoms in optical lattices provide a highly controllable and adaptable platform to study such new types of quantum matter. However, finding a clear route to realize non-Abelian quantum Hall states in these systems remains challenging. Here we use the density-matrix renormalization-group (DMRG) method to study the Hofstadter-Bose-Hubbard model at filling factor $\nu = 1$ and find strong indications that at $\alpha=1/6$ magnetic flux quanta per plaquette the ground state is a lattice analog of the continuum non-Abelian Pfaffian. We study the on-site correlations of the ground state, which indicate its paired nature at $\nu = 1$, and find an incompressible state characterized by a charge gap in the bulk. We argue that the emergence of a charge density wave on thin cylinders and the behavior of the two- and three-particle correlation functions at short distances provide evidence for the state being closely related to the continuum Pfaffian. The signatures discussed in this letter are accessible in current cold atom experiments and we show that the Pfaffian-like state is readily realizable in few-body systems using adiabatic preparation schemes.