Semiclassical Quantum Trajectories in the Monitored Lipkin-Meshkov-Glick Model

• URL: http://arxiv.org/abs/2407.20314v1
• Date: Mon, 29 Jul 2024 18:00:00 GMT
• Title: Semiclassical Quantum Trajectories in the Monitored Lipkin-Meshkov-Glick Model
• Authors: Alessandro Santini, Luca Lumia, Mario Collura, Guido Giachetti,
• Abstract summary: We investigate the dynamics of the Lipkin-Meshkov-Glick model, composed of $N$ all-to-all interacting spins $1/2$, under a weak external monitoring. We derive a set of semiclassical equations describing the evolution of the expectation values of global spin observables, which become exact in the thermodynamic limit. The transition is not affected by post-selection issues, as it is already visible at the level of ensemble averages.
• Score: 41.94295877935867
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Monitored quantum system have sparked great interest in recent years due to the possibility of observing measurement-induced phase transitions (MIPTs) in the full-counting statistics of the quantum trajectories associated with different measurement outcomes. Here, we investigate the dynamics of the Lipkin-Meshkov-Glick model, composed of $N$ all-to-all interacting spins $1/2$, under a weak external monitoring. We derive a set of semiclassical stochastic equations describing the evolution of the expectation values of global spin observables, which become exact in the thermodynamic limit. Our results shows that the limit $N\to\infty$ does not commute with the long-time limit: while for any finite $N$ the esamble average over the noise is expected to converge towards a trivial steady state, in the thermodynamic limit a MIPT appears. The transition is not affected by post-selection issues, as it is already visible at the level of ensemble averages, thus paving the way for experimental observations. We derive a quantitative theoretical picture explaining the nature of the transition within our semiclassical picture, finding an excellent agreement with the numerics.

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