Supersymmetry in the Fractional Quantum Hall Regime

Abstract

Supersymmetry (SUSY) is a symmetry transforming bosons to fermions and vice versa. Indications of its existence have been extensively sought after in high-energy experiments. However, signatures of SUSY have yet to be detected. In this manuscript we propose a condensed matter realization of SUSY on the edge of a Read-Rezayi quantum Hall state, given by filling factors of the form $\nu =\frac{k}{k+2}$, where $k$ is an integer. As we show, this strongly interacting state exhibits an $\mathcal{N}=2$ SUSY. This allows us to use a topological invariant - the Witten index - defined specifically for supersymmetric theories, to count the difference between the number of bosonic and fermionic zero-modes in a circular edge. In our system, we argue that the edge hosts $k+1$ protected zero-modes. We further discuss the stability of SUSY with respect to generic perturbations, and find that much of the above results remain unchanged. In particular, these results directly apply to the well-established $\nu =1/3$ Laughlin state, in which case SUSY is a highly robust property of the edge theory. These results unveil a hidden topological structure on the long-studied Read-Rezayi states.

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Cited by in corpus (9)

• Three-dimensional de Sitter horizon thermodynamics
• Realization of supersymmetry and its spontaneous breaking in quantum Hall edges
• Supersymmetry in Closed Chains of Coupled Majorana Modes
• Non-Relativistic Supergeometry in the Moore-Read Fractional Quantum Hall State
• Fermionic fractional quantum Hall states: A modern approach to systems with bulk-edge correspondence
• Operator-state correspondence in simple current extended conformal field theories: Toward a general understanding of chiral conformal field theories and topological orders
• 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
• Stability and response of trapped solitary wave solutions of coupled nonlinear Schrödinger equations in an external, $\mathcal{P}\mathcal{T}$- and supersymmetric potential
• Emergent Supersymmetry on the Edges