Charge transport, information scrambling and quantum operator-coherence in a many-body system with U(1) symmetry

• Published in: The journal of high energy physics 2023-05, Vol.2023 (5), p.37-33, Article 37
• Main Authors: Agarwal, Lakshya, Sahu, Subhayan, Xu, Shenglong
• Format: Article
• Language: English
• Subjects: 1/N Expansion; Charge density; Charge transport; Classical and Quantum Gravitation; Coherence; Elementary Particles; Fokker-Planck equation; High energy physics; Non-Equilibrium Field Theory; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Random Systems; Regular Article - Theoretical Physics; Relativity Theory; Spin dynamics; String Theory; Symmetry
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP05(2023)037

A bstract In this work, we derive an exact hydrodynamical description for the coupled, charge and operator dynamics, in a quantum many-body system with U(1) symmetry. Using an emergent symmetry in the complex Brownian SYK model with charge conservation, we map the operator dynamics in the model to the imaginary-time dynamics of an SU(4) spin-chain. We utilize the emergent SU(4) description to demonstrate that the U(1) symmetry causes quantum-coherence to persist even after disorder-averaging, in sharp contrast to models without symmetries. In line with this property, we write down a ‘restricted’ Fokker-Planck equation for the out-of-time ordered correlator (OTOC) in the large- N limit, which permits a classical probability description strictly in the incoherent sector of the global operator-space. We then exploit this feature to describe the OTOC in terms of a Fisher-Kolmogorov-Petrovsky-Piskun (FKPP)-equation which couples the operator with the charge and is valid at all time-scales and for arbitrary charge-density profiles. The coupled equations obtained belong to a class of models also used to describe the population dynamics of bacteria embedded in a diffusive media. We simulate them to explore operator-dynamics in a background of non-uniform charge configuration, which reveals that the charge transport can strongly affect dynamics of operators, including those that have no overlap with the charge.