The lowest wave function of the symmetrical many particles system

Yosuke Nagaoka, Tunemaru Usui

It is proved that, if the Hamiltonian of a system of spinless particles is symmetric with respect to interchange of the particles, the wave function with the lowest energy attainable without any restriction on its symmetry property, is symmetric with respect to interchange of the coordinates. It is also discussed what kind of conditions must be imposed upon the Hamiltonian for the theorem to be valid.

Ryan V. Mishmash, David F. Mross, Jason Alicea +1 more

We numerically assess model wave functions for the recently proposed particle-hole-symmetric Pfaffian (``PH-Pfaffian'') topological order, a phase consistent with the recently reported thermal Hall conductance [M. Banerjee et al., Nature 559, 205 (2018)] at the ever enigmatic $\ensuremath{\nu}=5/2$ quantum Hall plateau. We find that the most natural Moore-Read-inspired trial state for the PH-Pfaffian, when projected into the lowest Landau level, exhibits a remarkable numerical similarity on accessible system sizes with the corresponding (compressible) composite Fermi liquid. Consequently, this PH-Pfaffian trial state performs reasonably well energetically in the half-filled lowest Landau level, but is likely not a good starting point for understanding the $\ensuremath{\nu}=5/2$ ground state. Our results suggest that the PH-Pfaffian model wave function either encodes anomalously weak $p$-wave pairing of composite fermions or fails to represent a gapped, incompressible phase altogether.

Oktay Si̇nanoğlu

Mykhailo Yutushui, David F. Mross

We introduce a family of paired-composite-fermion trial wave functions for any odd Cooper-pair angular momentum. These wave functions are parameter-free and can be efficiently projected into the lowest Landau level. We use large-scale Monte Carlo simulations to study three cases: Firstly, the Moore-Read phase, which serves us as a benchmark. Secondly, we explore the pairing associated with the anti-Pfaffian and the particle-hole-symmetric Pfaffian. Specifically, we assess whether their trial states feature exponentially decaying correlations and thus represent gapped phases of matter. For Moore-Read and anti-Pfaffian we find decay lengths of ${\ensuremath{\xi}}_{\text{Moore-Read}}=1.30(5)$ and ${\ensuremath{\xi}}_{\text{anti-Pfaffian}}=1.38(14)$, in units of the magnetic length. By contrast, for the case of PH-Pfaffian, we find no evidence of a finite length scale for up to 56 particles.

Walter Greiner, Ludwig Neise, Horst Stöcker B