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

TL;DR

This paper investigates how entanglement measures in fractional quantum Hall states depend on the quasi-two-dimensional layer thickness, revealing different behaviors across various filling fractions and Landau levels, and providing insights into the nature of these states.

Contribution

It introduces a detailed analysis of entanglement entropy and spectrum considering finite layer thickness, highlighting differences between Landau levels and identifying the nature of the 5/2 state.

Findings

Entanglement measures vary with layer thickness and Landau level.

Laughlin states weaken or strengthen with thickness depending on the Landau level.

The 5/2 state shows entanglement consistent with a non-Abelian Moore-Read state.

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.