Slow Drive of Many-Body Localized Systems

Author: Mozgunov, Evgeny

Year: 2017

Degree: Dissertation (Ph.D.)

Advisor: Kitaev, Alexei

Committee Members: Kitaev, Alexei; Preskill, John P.; Kimble, H. Jeff; Brandao, Fernando

Option: Physics

DOI: 10.7907/Z9DJ5CND

Abstract

We investigate a many-body localized 1d spin chain with a Hamiltonian consisting of classical disordered Ising and a small transversal field. An existing perturbative diagonalization by Imbrie is simplified and reinterpreted in order to prove the anticipated form of the Lieb-Robinson bound and the area law in an eigenstate. We also show how to approximately reduce Imbrie’s unitary to a finite depth circuit. The concept of resonances in Imbrie’s work can be given a physical meaning as an avoided crossing of levels as functions of a magnetic field. For a slow drive of this field, we discuss the proofs of validity for an efficient classical simulation of such disordered systems, both isolated and in contact with the environment. Our results are applicable to Floquet systems and describe an unexpected mechanism of heating up over long times. We also revisit noisy quantum adiabatic annealers like the D-wave machine and find a nontrivial physics that can possibly be observed in them.

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