Entanglement Measures for Quasi-Two-Dimensional Fractional Quantum Hall States

Abstract

We theoretically examine entanglement in fractional quantum hall states, explicitly taking into account and emphasizing the quasi-two-dimensional nature of experimental quantum Hall systems. In particular, we study the entanglement entropy and the entanglement spectrum as a function of the finite layer thickness $d$ of the quasi-two-dimensional system for a number of filling fractions $\nu$ in the lowest and the second Landau levels: $\nu$ = 1/3, 7/3, 1/2, and 5/2. We observe that the entanglement measures are dependent on which Landau level the electrons fractionally occupy, and find that filling factions 1/3 and 7/3, which are considered to be Laughlin states, weaken with $d$ in the lowest Landau level ($\nu$=1/3) and strengthen with $d$ in the second Landau level ($\nu$=7/3). For the enigmatic even-denominator $\nu =5/2$ state, we find that entanglement in the ground state is consistent with that of the non-Abelian Moore-Read Pfaffian state at an optimal thickness $d$. We also find that the single-layer $\nu =1/2$ system is not a fractional quantum Hall state consistent with the experimental observation. In general, our theoretical findings based on entanglement considerations are completely consistent with the results based on wavefunction overlap calculations.

24 pages, 26 figures

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