1Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
2Trung tâm Vật lý lý thuyết Rudolf Peierls, Đại học Oxford, Oxford OX1 3PU, Vương quốc Anh
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Tóm tắt
We investigate the homogeneous chiral edge theory of the filling $nu=4/3$ fractional quantum Hall state, which is parameterized by a Luttinger liquid velocity matrix and an electron tunneling amplitude (ignoring irrelevant terms). We identify two solvable cases: one case where the theory gives two free chiral boson modes, and the other case where the theory yields one free charge $frac{2e}{sqrt{3}}$ chiral fermion and two free chiral Bogoliubov (Majorana) fermions. For generic parameters, the energy spectrum from our exact diagonalization shows Poisson level spacing statistics (LSS) in each conserved charge and momentum sector, indicating the existence of hidden conserved quantities and the possibility that the generic edge theory of the $nu=4/3$ fractional quantum Hall state is integrable. We further show that a global symmetry preserving irrelevant nonlinear kinetic term will lead to the transition of LSS from Poisson to Wigner-Dyson at high energies. This further supports the possibility that the model without irrelevant terms is integrable.
Tóm tắt phổ biến
Our 4/3 FQH edge system consists of two interacting chiral modes with inter-mode electron tunnelling, and we show it generically maps to an interacting chiral fermion model. At two special points, the model is integrable as free fermions or free bosons, respectively. Deviating from these points, we perform a detailed exact diagonalization (ED) study and detect the level spacing statistics (LSS) of the energy spectrum in a conserved charge sector. Generically, we find Poisson LSS, which indicates the existence of hidden conserved quantities and the possibility that the generic 4/3 FQH edge theory is integrable. We further identified a series of bilayer FQH states which are expected to have similar edge state integrability behaviors. Our results revealed a novel class of potentially robust integrable chiral systems beyond free (Luttinger) theories, and provide key insights for understanding the edge state thermalization and interferometric experiments in FQH systems.
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