Dissipative Floquet dynamics and measurement induced criticality in trapped-ion chains

G. Chiriaco,1,2 P. Sierant1,3, F. Surace1,2, S. Sharma1,2, X. Turkeshi1,2, M. Dalmonte1,2, R. Fazio1,4, G. Pagano5

1The Abdus Salam International Center for Theoretical Physics, Strada Costiera 11,
34151 Trieste, Italy

2SISSA — International School of Advanced Studies, via Bonomea 265, 34136 Trieste, Italy

3Institute of Theoretical Physics, Jagiellonian University in Krakow, Lojasiewicza 11,
30-348 Krakow, Poland

4Dipartimento di Fisica, Universita di Napoli “Federico II‘‘, Monte S. Angelo,
I-80126 Napoli, Italy

5Department of Physics and Astronomy, Rice University, 6100 Main Street, Houston,
TX 77005, USA

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 area law scaling is also present, and is distinct from the ordering transition. 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.

1. P. Sierant, G. Chiriaco et al. arXiv:2107.05669 (2021)

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