The basic problem of much of condensed matter physics, high energy physics, and quantum chemistry is to determine the ground state and dynamical properties of a many-body quantum system. How difficult is this problem? I will consider three different problems of determining dynamics and finding ground states for one dimensional quantum systems. In each case, the complexity of solving the problem will be closely related to the entanglement: systems with small quantum entanglement can be simulated efficiently while those with large entanglement are much harder to simulate. I will then discuss recent results on bounds on the entanglement, called area laws, which enable us to understand the remarkable success of a class of algorithms called matrix product state algorithms for these systems. Finally, I will discuss the possibility of finding similar algorithms for two dimensional quantum systems.
Coffee and cookies before the presentation at 3:15 pm, and refreshments after the presentation will both be served in Room 128.