Steve Simon

Abstract:

In this work, the second paper of this series, we study the (2+1)-dimensional version of a Hamiltonian model for topological phases based on higher-lattice gauge theory. We construct the ribbon operators that produce the pointlike excitations. These ribbon operators are used to find the braiding properties and topological charge carried by the pointlike excitations. The model also hosts looplike excitations, which are produced by membrane operators. By considering a change of basis, we show that, in certain cases, some looplike excitations represent domain walls between patches corresponding to different symmetry-related ground states, and we find this symmetry. We also map the higher-lattice gauge theory Hamiltonian to the symmetry-enriched string-net model for symmetry-enriched topological phases described by Heinrich, Burnell, Fidkowski, and Levin [Phys. Rev. B 94, 235136 (2016)], again in a subset of cases.

Abstract:

We perform the energy minimization of the paired composite fermion (CF) wave functions, proposed by Möller and Simon (MS) [Phys. Rev. B 77, 075319 (2008)] and extended by Yutushui and Mross (YM) [Phys. Rev. B 102, 195153 (2020)], where the energy is minimized by varying the CF pairing function, in the case of an approximate model of the Coulomb interaction in the second Landau level for pairing channels ℓ = −1, 3, 1, which are expected to be in the Pfaffian, anti-Pfaffian, and particle-hole symmetric (PH) Pfaffian phases, respectively. It is found that the energy of the ℓ = −1 MS wave function can be reduced substantially below that of the Moore-Read wave function at small system sizes; however, in the ℓ = 3 case the energy cannot be reduced much below that of the YM trial wave function. Nonetheless, both our optimized and unoptimized wave functions with ℓ = −1, 3 extrapolate to roughly the same energy per particle in the thermodynamic limit. For the ℓ = 1 case, the optimization makes no qualitative difference and these PH-Pfaffian wave functions are still energetically unfavorable. The effective CF pairing is analyzed in the resulting wave functions, where the effective pairing for the ℓ = −1, 3 channels is found to be well approximated by a weak-pairing BCS ansatz and the ℓ = 1 wave functions show no sign of emergent CF pairing.