Monday, December 16, 2019

10:30am

6C-442

Title: Bounds on entanglement entropy of ground states and scar states

speaker: Anurag Anshu (University of Waterloo)

abstract:

Relevant many-body quantum states, such as gapped ground states and gibbs state, can be approximated as polynomials of the underlying hamiltonian. This simple idea has been remarkably useful; such as in the proofs of 1D area laws and PEPS representation of gibbs state.  In this talk, we provide two new applications. First we show a subvolume law for frustration-free locally gapped spin systems in two dimensions, following the well known Approximate ground state projector (AGSP) approach. Our bound shows an entanglement entropy bound of approx L^{5/3}, for vertical and rectangular bipartitions of perimeter L.  Second, we show that recently studied scar quantum states have subvolume bound on entanglement entropy on lattices of finite dimension, complementing a recent result of Alhambra and Wilming.
  Based on joint works with Itai Arad and David Gosset and with Alvaro Alhambra.