Signatures of Supersymmetry in the $\nu =5/2$ Fractional Quantum Hall Effect

Abstract

The Moore-Read state, one of the leading candidates for describing the fractional quantum Hall effect at filling factor $\nu =5/2$, is a paradigmatic $p$-wave superconductor with non-Abelian topological order. Among its many exotic properties, the state hosts two collective modes: a bosonic density wave and a neutral fermion mode that arises from an unpaired electron in the condensate. It has recently been proposed that the descriptions of the two modes can be unified by postulating supersymmetry (SUSY) that relates them in the long-wavelength limit. Here we extend the SUSY description to construct wave functions of the two modes on closed surfaces, such as the sphere and torus, and we test the resulting states in large-scale numerical simulations. We demonstrate the equivalence in the long-wavelength limit between SUSY wave functions and previous descriptions of collective modes based on the Girvin-MacDonald-Platzman ansatz, Jack polynomials, and bipartite composite fermions. Leveraging the first-quantized form of the SUSY wave functions, we study their energies using the Monte Carlo method and show that realistic $\nu =5/2$ systems are close to the putative SUSY point, where the two collective modes become degenerate in energy.

Main text 6 pages, 4 figures with attached supplementary information

References in corpus (19)

• Non-Abelian Anyons and Topological Quantum Computation
• Direct observation of anyonic braiding statistics at the $\nu$=1/3 fractional quantum Hall state
• Fractional statistics in anyon collisions
• Particle-hole symmetry and the Pfaffian state
• Particle-Hole Symmetry and the $\nu =5/2$ Quantum Hall State
• Orbital Landau level dependence of the fractional quantum Hall effect in quasi-two dimensional electron layers: finite-thickness effects
• Spontaneous Particle-Hole Symmetry Breaking in the $\nu =5/2$ Fractional Quantum Hall Effect
• Neutral Fermion Excitations in the Moore-Read state at ν=5/2
• Quantum Phase Transitions and the ν=5/2 Fractional Hall State in Wide Quantum Wells
• Numerical Calculation of the Neutral Fermion Gap at $\nu =5/2$
• Fractional Quantum Hall Effect at $\nu =2+4/9$
• A non-Abelian parton state for the $\nu =2+3/8$ fractional quantum Hall effect
• Fractional quantum Hall state at ν=1/4 in a wide quantum well
• ${\mathbb{Z}}_n$ superconductivity of composite bosons and the $7/3$ fractional quantum Hall effect
• Realization of supersymmetry and its spontaneous breaking in quantum Hall edges
• Collective excitations at filling factor 5/2: The view from superspace
• Hall Viscosity of Composite Fermions
• Supergravity model of the Haldane-Rezayi fractional quantum Hall state
• Non-Relativistic Supergeometry in the Moore-Read Fractional Quantum Hall State

Cited by in corpus (9)

• Microscopic Model for Fractional Quantum Hall Nematics
• Static structure factor and the dispersion of the Girvin-MacDonald-Platzman density mode for fractional quantum Hall fluids on the Haldane sphere
• Deformed Fredkin model for the $\nu =5/2$ Moore-Read state on thin cylinders
• Gauging or extending bulk and boundary conformal field theories: Application to bulk and domain wall problem in topological matter and their descriptions by (mock) modular covariant
• Dispersion of neutral collective modes in partonic fractional quantum Hall states and its applications to paired states of composite fermions
• Engineering of Anyons on M5-Probes via Flux Quantization
• Dispersion of collective modes in spinful fractional quantum Hall states on the sphere
• Massive Higher-Spin Fields in the Fractional Quantum Hall Effect
• Spin of fractional quantum Hall neutral modes and "missing states" on a sphere