Multiple Gravitons and spectral sum rules in Fractional Quantum Hall systems

Abstract: In this talk, I will provide the historical review of magneto-roton excitation, which is the gapped neutral excitation in the Lowest Landau Level. The magneto-roton mode has spin-2 and can be considered as a massive graviton mode in 2+1D [1]. This spin-2 mode plays a central role in the physics of FQH. In the current literature, the spin-2 mode of Jain's sequences near filling fraction 1/2 can be thought of as the shear deformation of the composite fermion Fermi surface [2]. In this talk, I will show that for Jain's sequences near filling fraction 1/4, there will be an extra massive graviton mode [3]. The extra mode was proposed in our recent work on the Dirac composite fermion theory of general Jain's sequences in order to satisfy the Haldane bound of the static structure factor. The extra mode was confirmed numerically recently with the guidance of FQH sum rules [4]. I will briefly discuss our physical interpretation of the new massive graviton mode. If time allows, I will describe the experimental setup that can detect the graviton modes [5].

References:

[1] Siavash Golkar, Dung X. Nguyen and Dam T. Son JHEP 021, 01 (2016)

[2] DX Nguyen, A Gromov, DT Son, Physical Review B 97 (19), 195103 (2018)

[3] DX Nguyen, DT Son, arXiv:2105.02092 (2021)

[4] DX Nguyen, Edward Rezayi, Dam T. Son and Kun Yang To appeared (Arxiv:2111.xxxxx)

[5] DX Nguyen, DT Son, Phys. Rev. Research 3, 023040 (2021)

condensed mattermathematical physics

Audience: researchers in the topic

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