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

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-Plank 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 property 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. Following this, we simulate the coupled equations of motion and explore operator-dynamics in a background of non-uniform charge configuration. We find that the charge transport can strongly affect dynamics of operators, including those that have no overlap with the charge.

Information scrambling and entanglement dynamics of complex Brownian Sachdev-Ye-Kitaev models

“…There are many interesting generalizations of the current work. Firstly, it is interesting to consider the late-time information scrambling of cBSYK chains [73]. This requires a complete solution of (3.9) with a generalization of (2.23).…”