Re-entrant Anomalous Quantum Hall Phase of 5/2 State*

Recent thermal Hall conductivity [1] and shot noise [2] measurements have revealed the true topological nature of the enigmatic 5/2 state to be the particle-hole symmetric Pfaffian (PH-Pf) order, which contradicts most theoretical predictions of Pfaffian or anti-Pfaffian orders. In an intermediate range of Landau level mixing strength, we find [3] a re-entrant anomalous phase (A-phase) which is topologically different from all the above topological orders. This A-phase has a unique topology that is adiabatically connected to all the Pfaffian, anti-Pfaffian, and PH-Pf flux shifts (not to be confused with topological orders) as the corresponding entanglement spectra appear to be similar. We propose a wave function for this A-phase, having the same flux shift of PH-Pf order but without particle-hole symmetry. In the A-phase this wave function has extremely high overlap with the exact ground state for the PH-Pf shift and non-ignorable overlaps with the exact ground states for Pfaffian and Anti-Pfaffian shifts, and further shows a high degree of matching of low-lying entanglement spectra with the same for the exact state. Analyzing the topological properties of the proposed wave function, we find the thermal Hall conductance of 5/2 unit, in agreement to experiment [1].

[1] M. Banerjee et al. Nature 559, 205–210 (2018)

[2] B. Dutta et al. Science 375, 193 (2022)

[3] S. Das, S. Das, and S. S. Mandal, arXiv: 2206.04419