Entanglement entropy and hyperuniformity of determinantal point processes
A talk in the Seminar Zufallsmatrizen series by
Luis Daniel Abreu
| Abstract: | We will show that, under a condition on the Schatten p norms (p<1) of the
Toeplitz operator associated with the kernel of a DPP, whose symbol is the
indicator function of a domain, the bipartite entanglement entropy is
proportional to the variance. This leads to equivalences between
hyperuniformity classes and classes of growth for the entanglement entropy
(area law and area law with log correction). Examples include the fermionic
model in several dimensions considered by Gioev and Klich (PRL, 2006), which is
a multidimensional version of the sine DPP, where a log correction to the area
law shows up; the fermionic model on Riemann surfaces of Charles and Estienne
(CMP, 2020, a work which strongly influenced this research), the infinite Ginibre
process and its polyanalytic versions in higher Landau levels, which belong to
the large class of Weyl-Heisenberg ensembles, a DPP defined via the action of
the Heisenberg group, dependent on a function g (for choices of g within
Hermite functions we are led to the mentioned Ginibre-type ensembles). These
last classes of DPPs enjoy an area law as a consequence of their Class I
hyperuniformity. Please contact Lucas Hackl (Lucas.Hackl@unimelb.edu.au) for details regarding access Within the CRC this talk is associated to the project(s): C6 |