Computing quantum thermalization dynamics: from quantum chaos to emergent hydrodynamics
Condensed Matter seminars
Friday 16 June 2017
to 14:00 at
112:028 (Nordita South)
Ehud Altman (Berkely)
The long time dynamics of generic strongly interacting quantum systems presents a fundamental challenge for theory and computation. The main obstruction to numerical solution of this problem is the linear growth of the entanglement entropy in time, which implies exponential growth of the computational resources. In this talk I will discuss a new approach to overcome this obstruction and accurately describe the chaotic dynamics and emergent hydrodynamic behavior at long times using matrix product states. In our scheme we utilize the time dependent variational principle to truncate "non-useful" entanglement while retaining crucial information on local observables. I will present results for thus obtained transport coefficients and chaos characteristics in the Ising model subject to both transverse and longitudinal fields.
Time permitting I will also discuss systems, which saturate the quantum bound on chaos. Using the SYK model as an example, I will argue that the temperature dependence of the Lyapunov exponent in such maximally chaotic systems is described by a classical theory and has a geometric origin.