|タイトル||Area-law conjecture for entanglement entropy|
|開催日時||2019年5月16日 13:00 - 14:00 + 30 min|
|場所||Keio Univ. Yagami-campus Bldg.14th, 6F
|内容|| In quantum computation, one of the primary problems is to solve the local Hamiltonian problem, namely finding the ground state (i.e., the lowest energy state) for a given many-body Hamiltonian. The problem is known to be the QMA complete problem in general . On the other hand, from many numerical studies, the most important class, where the ground state has a spectral gap, is expected to be efficiently solved. This class corresponds to non-critical ground states and determines quantum phases of matter. In the analysis of this class, the entanglement entropy (or Von-Neumann entropy in subsystem) plays a central role. The area-law conjecture states that it is proportional to the surface region of subsystem if the ground state is gapped. This conjecture is a backbone of most of the classical algorithms such as the density-matrix-renormalization group  as well as classification of the quantum phases. Despite much effort on this conjecture, the area law is mathematically proved in highly limited cases [3,4,5]. In the present talk, I will give an overview of the conjecture, and show our recent achievement if the time allows.
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