2016/12/31 by Tianci Zhou, David J. Luitz · 2 citations
Computer Science · Mathematics · Physics and Astronomy · #Chaotic #Computer science #Entropy (arrow of time) #Floquet theory #Hilbert space #Law #Logarithmic growth #Mathematical analysis #Mathematics #Model Reduction and Neural Networks #Neural Networks and Reservoir Computing #Operator (biology) #Physics #Quantum #Quantum entanglement #Quantum many-body systems #Quantum mechanics #Statistical physics #Time evolution #Unitary operator #Unitary state #cond-mat.stat-mech
paper · pdf · doi:10.1103/physrevb.95.094206
published as Phys. Rev. B 95, 094206 (2017) · 18 pages, 14 figures. Revised version has added a refined argument and numerical evidence for the deficit value in the disordered Heisenberg model
openalex created_date 2017/01/06 · arxiv created 2017/03/23 · openalex publication_date 2017/03/23 · arxiv updated 2017/03/27 · openalex updated_date 2026/08/06
Entanglement entropy is a widely applicable indicator of the onset of quantum chaos. In particular, the entanglement entropy of the wave function after a quench from an initial state with low entanglement can be used to study the thermalization of the system. Here, the authors propose an initial-state independent quantity called the ``operator entanglement entropy'' (opEE) to extract the properties of the unitary evolution operator. They study the growth of the opEE in Floquet, chaotic, and many-body localized systems. They respectively have a linear, power-law, and logarithmic growth before reaching extensive saturation values. The most chaotic Floquet spin model has the maximal saturation value among the three classes and is identical to the value of a random unitary operator (the Page value). The authors interpret the opEE as the state EE of a quenched state living in a doubled Hilbert space, thus establishing its consistency with the existing state EE results. They conclude that the EE of the evolution operator should characterize the propagation of information in these systems.