Description
We numerically study the behavior of spin-1/2 fermions on a
two-dimensional square lattice subject to a uniform magnetic
field, where opposite spins interact via an on-site
attractive interaction. The single-particle Hamiltonian is
the Harper-Hofstadter model which was recently realized in
several cold atomic gas experiments using artificial gauge
fields. In this context, a Feschbach resonance can be used
to implement a highly tunable on-site interaction. Starting
from the non-interacting case where each spin population is
prepared in a quantum Hall state with unity filling, we
follow the evolution of the system as the interaction
strength is increased. Above a critical value and for
sufficiently low flux density, we observe the emergence of a
twofold quasidegeneracy accompanied by the opening of an
energy gap to the third level. Analysis of the entanglement
spectra shows that the gapped ground state is the bosonic
1/2 Laughlin state. Our work therefore provides compelling
evidence of a topological phase transition from the
fermionic integer quantum Hall state to the bosonic Laughlin
state at a critical attraction strength. I will present the
numerical signatures of these two phases, and analyze the
equilibrium properties of the phase transition. Finally, I
will discuss some preliminary results concerning the
dynamics of the phase transition.
Ref: Creating a bosonic fractional quantum Hall state by
pairing fermions, C. Repellin, T. Yefsah, A. Sterdyniak,
arXiv:1612.09184
