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

• URL: http://arxiv.org/abs/2210.14828v3
• Date: Wed, 30 Nov 2022 16:57:34 GMT
• Title: Charge transport, information scrambling and quantum operator-coherence in a many-body system with U(1) symmetry
• Authors: Lakshya Agarwal, Subhayan Sahu, Shenglong Xu
• Abstract summary: We derive an exact hydrodynamical description for the coupled, charge and operator dynamics in a quantum many-body system with U(1) symmetry. We utilize the emergent SU(4) description to demonstrate that the U(1) symmetry causes quantum-coherence to persist even after disorder-averaging.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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