Speaker
Emil Bergholtz
(Max Planck Institute for the Physics of Complex Systems)
Description
We present a new approach for obtaining the scaling
behavior of the entanglement entropy in fractional
quantum Hall (FQH) states from finite-size wavefunctions.
By employing the torus geometry and the fact that the
torus aspect ratio can be readily varied, we can extract the
entanglement entropy of a spatial block as a continuous
function of the block boundary length. This approach allows
us to extract the topological entanglement entropy with an
accuracy superior to that possible for the spherical or disc
geometry, where no natural continuously variable
parameter is available. Other than the topological
information, the study of entanglement scaling is also
useful as an indicator of the difficulty posed by FQH states
for various numerical techniques. We also analyze the
entanglement spectrum of Laughlin states on the torus and
show that it is arranged in towers, each of which is
generated by modes of two spatially separated chiral edges.
This structure is present for all torus circumferences, which
allows for a microscopic identification of the prominent
features of the spectrum by perturbing around the thin-
torus limit.
