English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Neutral excitations in a fractional quantum Hall droplet define theincompressibility gap of the topological phase. In this work, we derived a setof analytical results for the energy gap of the graviton modes with two-bodyand three-body Hamiltonians in both the long-wavelength and thermodynamiclimit. These allow us to construct model Hamiltonians for the graviton modes indifferent FQH phases, and to elucidate a hierarchical structure of conformalHilbert spaces (nullspaces of model Hamiltonians) with respect to the gravitonmodes and their corresponding ground states. Using the analytical toolsdeveloped, we perform numerical analysis with a particular focus on theLaughlin $\nu = 1/5$ and the Gaffnian $\nu = 2/5$ phases. Our calculation showsthat for gapped phases, low-lying neutral excitations can undergo a "phasetransition" even when the ground state is invariant. We discuss thecompressibility of the Gaffnian phase, the possibility of multiple gravitonmodes, and the transition from the graviton modes to the "hollow-core" modes,as well as their experimental consequences.

Analytic exposition of the graviton modes in fractional quantum Hall effects and its physical implications