Quantum geometric fluctuations in fractional quantum Hall fluids

TL;DR

This paper develops a comprehensive microscopic theory of geometric excitations in fractional quantum Hall fluids, explaining their properties, relation to ground state density modulations, and potential experimental detection, including graviton modes.

Contribution

It introduces a detailed microscopic framework for geometric modes in FQH fluids, connecting them to physical properties and experimental observables, and explains their universal and non-universal features.

Findings

Analytic expressions for chirality, multiplicity, and energy of geometric modes.

Prediction of measurable geometric or graviton modes in various phases.

Existence of gapped geometric modes in compressible FQH phases.

Abstract

We present here a complete microscopic theory of a family of neutral excitations in the fractional quantum Hall fluids, related to the geometric fluctuations of the quantum Hall ground states. Many of the physical properties of such geometric modes can be inferred analytically. These include the chirality, multiplicity and energy of these geometric modes, as well as the relationship to the density modulation of the ground states of both incompressible and compressible fluids, with or without translational symmetry (e.g. the bubble and stripe phases). With a particular focus on the recently experimentally measured graviton modes as the special case, we elucidate both the universal aspects of the geometric modes and the non-universal aspects dependent on the details of the microscopic Hamiltonians. The microscopic theory explains some of the phenomenological components in the effective field theory and composite fermion theory. It predicts how geometric or graviton modes of both chiralities can be measured in experiments for any topological or compressible phases at different energy scales. In particular we show gapped geometric modes can exist even for compressible FQH phases, though translational symmetry of the ground state is important for such modes to couple to external probes (e.g. Raman scattering) in the long wavelength limit.