Geometric Fluctuation of Conformal Hilbert Spaces and Multiple Graviton Modes in Fractional Quantum Hall Effect

TL;DR

This paper develops a microscopic theory linking geometric fluctuations in conformal Hilbert spaces to multiple graviton-like modes in fractional quantum Hall fluids, verified numerically and relevant for experiments.

Contribution

It introduces a microscopic framework for multiple graviton modes in FQH fluids based on geometric fluctuations of conformal Hilbert spaces, with numerical validation.

Findings

Multiple graviton modes are associated with geometric fluctuations of conformal Hilbert spaces.

Numerical verification confirms the theory for model and realistic interactions.

The theory informs the understanding of Haldane modes and their experimental relevance.

Abstract

Neutral excitations in fractional quantum Hall (FQH) fluids define the incompressibility of topological phases, a species of which can show graviton-like behaviors and are thus called the graviton modes (GMs). Here, we develop the microscopic theory for multiple GMs in FQH fluids and show explicitly that they are associated with the geometric fluctuation of well-defined conformal Hilbert spaces (CHSs), which are hierarchical subspaces within a single Landau level, each with emergent conformal symmetry and continuously parameterized by a unimodular metric. This leads to several statements about the number and the merging/splitting of GMs, which are verified numerically with both model and realistic interactions. We also discuss how the microscopic theory can serve as the basis for the additional Haldane modes in the effective field theory description and their experimental relevance to realistic electron-electron interactions.