High temperature adiabatic flows in ergodic systems
Presented by Anatoli Polkovnikov, Boston University
I will discuss the structure of local generators of adiabatic transformations in ergodic Hamiltonians. These generators play a key role in many different setups like finding quantum speed limit bounds, quantum information geometry, shortcuts to adiabaticity, Schrieffer Wolff transformations, Floquet Hamiltonians, Wilson-Wegner flows and many more. While mathematically these generators are ill defined in quantum chaotic systems, they can allow for very accurate local approximations in certain directions. Using an example of a specific nonintegrable Ising chain I will show that these generators are highly anisotropic allowing one to define adiabatic flows connecting families of Hamiltonians. These flows are very reminiscent of Renormalization Group flows. I will also show that near singular (massively
degenerate) points one can define special (dark) states which are very stable to adiabatic deformations. Such special states are analogous to recently discovered quantum scars.
3:30 pm, Thursday, October 24, 2019
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