Tripartite Information and Scrambling in Quantum Many-Body Systems

by Niklas Bölter
Doctoral thesis
Date of Examination:2023-05-09
Date of issue:2023-05-11
Advisor:Prof. Dr. Stefan Kehrein
Referee:Prof. Dr. Stefan Kehrein
Referee:PD Dr. Salvatore R. Manmana
Persistent Address: http://dx.doi.org/10.53846/goediss-9879

 

 

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Abstract

English

This thesis contributes to the study of quantum chaos and thermalization of closed quantum systems by applying tools from quantum information theory. We study scrambling – the delocalization of quantum information – in one-dimensional quantum many-body systems using the observable-independent tripartite information 𝐼3. We consider closed quantum systems that undergo unitary time evolution governed by a Hamiltonian, and compare them to the strong scrambling caused by random unitary operators (Haar scrambling). The tripartite information is a tool from quantum information theory that allows us to quantify correlations in space and time by considering the unitary operator evolving the system as a state |𝑈 (𝑡)⟩ in a doubled Hilbert space H ⊗ H. We found a ballistic spreading of information in translation invariant systems of spinless fermions that causes Haar scrambling in interacting models. For strongly disordered versions of the XXZ chain and the transverse-field Ising chain we found a complete breakdown of in- formation transport in non-interacting Anderson localized systems, as well as a logarithmically slow spreading of the information signal in systems that are said to be many-body localized (MBL).
Keywords: Quantum Chaos; Thermalization; Many-body quantum systems; Information Theory; Scrambling; Quantum Information Theory
 
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