Kavli Affiliate: Joel E. Moore
| First 5 Authors: Jyesta M. Adhidewata, Jyesta M. Adhidewata, , ,
| Summary:
The excitations of fractional quantum Hall effect (FQHE) states have been
largely inaccessible to experimental probes until recently. New electron
scanning tunneling microscopy (STM) results from Hu et.al. (2023) show promise
in detecting and identifying these excited states via the local density of
states (LDOS) spectrum. On a torus, there exists a mapping to a 1D lattice
Hamiltonian with center-of-mass or dipole moment conservation. In this work, we
apply perturbation theory starting from the thin cylinder limit ($L_x
rightarrow infty, L_y <l_B$ for torus dimensions $L_x$ and $L_y$) to obtain
an analytical approach to the low-lying neutral and charged excitations of the
$nu =1/3$ FQHE state. Notably, in the thin cylinder we can systematically
enumerate all the low-lying excitations by the patterns of ‘dipoles’ formed by
the electron occupation pattern on the 1D lattice. We find that the
thin-cylinder limit predicts a significant dispersion of the low-lying neutral
excitations but sharpness of the LDOS spectra, which measure charged
excitations. We also discuss connections between our work and several different
approaches to the FQHE STM spectra, including those using the composite fermion
theory. Numerical exact diagonalization beyond the thin-cylinder limit suggests
that the energies of charged excitations remain largely confined to a narrow
range of energies, which in experiments might appear as a single peak.
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