Supergravity model of the Haldane-Rezayi fractional quantum Hall state

TL;DR

This paper introduces a supergravity model to describe the low-energy physics of the Haldane-Rezayi fractional quantum Hall state, revealing emergent gravitons and gravitinos supported by numerical evidence.

Contribution

It presents the first supergravity framework for a quantum Hall state, linking high-energy physics concepts with condensed matter phenomena.

Findings

Edge modes and algebra naturally emerge in the supergravity model.

Numerical calculations support emergent graviton and gravitino excitations.

The model provides a novel theoretical approach to exotic quantum Hall states.

Abstract

Supersymmetry and supergravity were invented in the 1970s to solve fundamental problems in high-energy physics. Even though neither of these ideas has yet been confirmed in high-energy and cosmology experiments, they have been beneficial in constructing numerous theoretical models, including superstring theory. Despite the absence of supersymmetry in particle physics, it can potentially emerge in exotic phases of strongly correlated condensed matter systems. In this paper, we propose a supergravity model that describes the low-energy physics of the Haldane-Rezayi state, a gapless quantum Hall state that occurs in a half-filled Landau level. We show that the corresponding edge modes of the Haldane-Rezayi state and the Girvin-MacDonald-Platzman algebra appear naturally in the supergravity model. Finally, we substantiate our theoretical findings with numerical exact diagonalization calculations that support the appearance of the emergent graviton and gravitino excitations in the Haldane-Rezayi state.