Geometric fluctuation of conformal Hilbert spaces and multiple graviton modes in fractional quantum Hall effect

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.

Self-similarity of spectral response functions for fractional quantum Hall states

“…Since the structure factor defined in equation (3.8) conserves particle number, these plots show the coupling of the ground state to gapped excitations and consist of a spectrum of peaks at finite frequency. As expected: the structure factor corresponding to the V 1 interaction yields a broader spread of frequencies, due to the normalization of the V 1 = 1 pseudopotential [14]; the relative peak amplitudes are consistent in the two cases, owing to the dominant V 1 component of the Coulomb interaction [13,16]; and the shape of both distributions is unimodal, according to the theory for Laughlin states. 3 slight variations in the number and heights of the peaks, the overall shape of the envelope holds for all runs and for all q y , and there is a close resemblance between the structure factors of these two FQH states.…”

“…via surface acoustic waves [10,11], and analysed using Raman scattering to reveal additional spin properties [12]. Despite its rich structure and experimental applicability, however, numerical studies that systematically investigate the spectral response of FQH states have only recently gained traction [5,8,[13][14][15][16][17].…”

“…In the literature, these collective peaks are typically q x -momentum-resolved and may sometimes be referred to simply as peaks[14,15], or collective modes[13,16] in certain contexts.…”

Fermionic fractional quantum Hall states: A modern approach to systems with bulk-edge correspondence

“…Before going to the next section, we give a brief comment on the reason why the Laughlin state is so ubiquitous even when considering gapless FQHE such as the Gaffnian CFT [32,81,111,112]. It is easy to obtain a modular invariant, Eq.…”