Renormalization of Quantum Operations: Parity-Time Transition and Chaotic Flows

TL;DR

This paper extends the renormalization group framework to nonunitary quantum dynamics, revealing chaotic flows and parity-time transitions driven by the interplay of decoherence and coherence, with implications for experimental quantum systems.

Contribution

It introduces a real-time coarse-graining RG approach for nonunitary quantum dynamics, highlighting the role of chaos and parity-time transitions in such systems.

Findings

Chaotic RG flows emerge when coherent dynamics dominate.

Parity-time transition acts as a prototype in nonunitary quantum systems.

The measurement-induced transition belongs to the Yang-Lee edge universality class.

Abstract

The renormalization group (RG) in statistical physics focuses on ground-state properties of equilibrium systems. However, it is unclear how it should be generalized to nonunitary quantum dynamics caused by dissipation and measurement backaction, in which the notion of conserved energy is absent. Here, we extend the RG to cover nonunitary quantum dynamics governed by quantum operations. By performing coarse-graining in real time, we find that the competition between decoherence and coherent dynamics plays a decisive role in the behavior of the RG flow. In particular, we find that chaotic behavior without fixed points emerges in the RG flow when coherent dynamics is dominant, with the parity-time transition serving as a prototypical example. The measurement-induced parity-time transition belongs to the universality class of the one-dimensional Yang-Lee edge singularity, which serves as a guide for experimentally realizing imaginary fields in lattice spin systems with a quantum system.