Area laws and approximations of quantum many-body states

8 01/2015

Thursday, 08 Jan. 2015, 14:00 - 15:00

Workgroup Verstraete Group

Presenter: Yinmin Ge
Host: F. Verstraete
Where: Office F. Verstraete

It is commonly believed that area laws for entanglement entropies imply that a quantum many-body state can be faithfully represented by efficient tensor network states - a conjecture frequently stated in the context of numerical simulations and analytical considerations. In this talk, I will show that this is in general not the case, except in one dimension. It turns out that the set of quantum many-body states which satisfy an area law for all Renyi entropies contains a subspace of exponential dimension. Thus, there are states satisfying area laws for all Renyi entropies but still cannot be approximated by states with a classical description of small Kolmogorov complexity, including efficient tensor network states such as polynomial PEPS or MERA. Not even a quantum computer with post-selection can efficiently prepare all quantum states fulfilling an area law, and moreover not all area law states can be eigenstates of local Hamiltonians. I will also discuss variations of these results with translational and rotational invariance as well as decaying correlations. This is joint work with Jens Eisert.[1]

[1] Y. Ge, J. Eisert, http://arxiv.org/abs/1411.2995