Dissipative Floquet Dynamics: from Steady State to Measurement Induced Criticality in Trapped-ion Chains

TL;DR

This paper explores how dissipative Floquet dynamics in trapped-ion chains can lead to various non-equilibrium phase transitions, including measurement-induced entanglement transitions and magnetic ordering, with implications for quantum error correction and Zeno effects.

Contribution

It introduces a framework using many-body dissipative Floquet dynamics to analyze both dissipative and measurement-induced phase transitions in long-range and short-range quantum systems.

Findings

A phase transition between ferromagnetic and paramagnetic phases in long-range systems.

A measurement-induced entanglement transition from volume law to sub-volume law.

Enhanced entanglement volume law phase in short-range interactions.

Abstract

Quantum systems evolving unitarily and subject to quantum measurements exhibit various types of non-equilibrium phase transitions, arising from the competition between unitary evolution and measurements. Dissipative phase transitions in steady states of time-independent Liouvillians and measurement induced phase transitions at the level of quantum trajectories are two primary examples of such transitions. Investigating a many-body spin system subject to periodic resetting measurements, we argue that many-body dissipative Floquet dynamics provides a natural framework to analyze both types of transitions. We show that a dissipative phase transition between a ferromagnetic ordered phase and a paramagnetic disordered phase emerges for long-range systems as a function of measurement probabilities. A measurement induced transition of the entanglement entropy between volume law scaling and sub-volume law scaling is also present, and is distinct from the ordering transition. The two phases correspond to an error-correcting and a quantum-Zeno regimes, respectively. The ferromagnetic phase is lost for short range interactions, while the volume law phase of the entanglement is enhanced. An analysis of multifractal properties of wave function in Hilbert space provides a common perspective on both types of transitions in the system. Our findings are immediately relevant to trapped ion experiments, for which we detail a blueprint proposal based on currently available platforms.