Geometric entanglement in integer quantum Hall states
- URL: http://arxiv.org/abs/2009.02337v1
- Date: Fri, 4 Sep 2020 18:00:19 GMT
- Title: Geometric entanglement in integer quantum Hall states
- Authors: Benoit Sirois, Lucie Maude Fournier, Julien Leduc, William
Witczak-Krempa
- Abstract summary: We study the quantum entanglement structure of integer quantum Hall states via the reduced density matrix of spatial subregions.
We focus on an important class of regions that contain sharp corners or cusps, leading to a geometric angle-dependent contribution to the EE.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: We study the quantum entanglement structure of integer quantum Hall states
via the reduced density matrix of spatial subregions. In particular, we examine
the eigenstates, spectrum and entanglement entropy (EE) of the density matrix
for various ground and excited states, with or without mass anisotropy. We
focus on an important class of regions that contain sharp corners or cusps,
leading to a geometric angle-dependent contribution to the EE. We unravel
surprising relations by comparing this corner term at different fillings. We
further find that the corner term, when properly normalized, has nearly the
same angle dependence as numerous conformal field theories (CFTs) in two
spatial dimensions, which hints at a broader structure. In fact, the Hall
corner term is found to obey bounds that were previously obtained for CFTs. In
addition, the low-lying entanglement spectrum and the corresponding
eigenfunctions reveal "excitations" localized near corners. Finally, we present
an outlook for fractional quantum Hall states.
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