Fig. 2: Multiple graviton modes and composite fermionization. | Nature Communications

Fig. 2: Multiple graviton modes and composite fermionization.

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

Fig. 2: Multiple graviton modes and composite fermionization.The alternative text for this image may have been generated using AI.

a An illustration of the hierarchical structure of three CHSs and the ground state \(\left|{\psi }_{0}\right\rangle\) within \({{{{{{{{\mathcal{H}}}}}}}}}_{{{{{{{{\rm{III}}}}}}}}}\) (red sphere) in the Hilbert space. The corresponding GMP mode \(|{\psi }_{g}\rangle\) is outside \({{{{{{{{\mathcal{H}}}}}}}}}_{{{{{{{{\rm{I}}}}}}}}}\) so one can imagine the regularized guiding center density operator acting on the ground state goes through three CHSs, leading to three emergent GMs because of the fluctuation around the metric of each of the CHSs. b PH conjugate of Laughlin states within different CHSs. Here, \({{{{{{{{\mathcal{C}}}}}}}}}_{i}\) denotes the PH conjugate within \({{{{{{{{\mathcal{H}}}}}}}}}_{i}^{2{{{{{{{\rm{bdy}}}}}}}}}\), and \({{{{{{{\mathcal{C}}}}}}}}\) denotes the PH conjugate within a single LL or a single CF level. Arrows represent magnetic fluxes, and the CFs denoted by \({{{{{{{{\rm{cf}}}}}}}}}_{{\nu }^{*}}^{n}\), consisted of one electron and n fluxes, form a CF FQH state at ν*. Note that the red (\({{{{{{{{\rm{cf}}}}}}}}}_{4/5}^{2}\)) and the yellow (\({{{{{{{{\rm{cf}}}}}}}}}_{2/3}^{4}\)) CFs are anti-CFs with the fluxes opposite to the external field.

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