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arXiv · 2309.17003

Energy minimization of paired composite fermion wave functions in the spherical geometry

Greg J. Henderson·Gunnar Möller·Steven H. Simon
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Abstract

We perform the energy minimization of the paired composite fermion (CF) wave functions, proposed by M\"oller and Simon (MS) [PRB 77, 075319 (2008)] and extended by Yutushui and Mross (YM) [PRB 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 $\ell = -1, 3, 1$ 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 $\ell = -1$ MS wave function can be reduced substantially below that of the Moore-Read wave function at small system sizes, however, in the $\ell = 3$ case the energy cannot be reduced much below that of the YM trial wavefunction. Nonetheless, both our optimized and unoptimized wavefunctions with $\ell=-1,3$ extrapolate to roughly the same energy per particle in the thermodynamic limit. For the $\ell = 1$ case, the optimization makes no qualitative difference and these PH-Pfaffian wave functions are still energetically unfavourable. The effective CF pairing is analyzed in the resulting wave functions, where the effective pairing for the $\ell = -1, 3$ channels is found to be well approximated by a weak-pairing BCS ansatz and the $\ell = 1$ wave functions show no sign of emergent CF pairing.

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Greg J. Henderson, Gunnar Möller, Steven H. Simon. 2023-09-29. Energy minimization of paired composite fermion wave functions in the spherical geometry. https://doi.org/10.1103/physrevb.108.245128

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