Thermodynamic phases in first detected return times of quantum many-body systems

• URL: http://arxiv.org/abs/2311.05585v2
• Date: Thu, 14 Mar 2024 16:34:51 GMT
• Title: Thermodynamic phases in first detected return times of quantum many-body systems
• Authors: Benjamin Walter, Gabriele Perfetto, Andrea Gambassi,
• Abstract summary: We study the probability distribution of the first return time to the initial state of a quantum many-body system. We show that this distribution can be interpreted as a continuation of the canonical partition function of a spin chain with non-interacting domains at equilibrium.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We study the probability distribution of the first return time to the initial state of a quantum many-body system subject to stroboscopic projective measurements. We show that this distribution can be interpreted as a continuation of the canonical partition function of a spin chain with non-interacting domains at equilibrium, which is entirely characterised by the Loschmidt amplitude of the quantum many-body system. This allows us to show that this probability may decay either algebraically or exponentially asymptotically in time, depending on whether the spin model displays a ferromagnetic or a paramagnetic phase. We illustrate this idea on the example of the return time of $N$ adjacent fermions in a tight-binding model, revealing a rich phase behaviour, which can be tuned by scaling the probing time with $N$. Our analytical predictions are corroborated by exact numerical computations.

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