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arXiv · 2311.05585

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

Benjamin Walter·Gabriele Perfetto·Andrea Gambassi
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Abstract

We study the probability distribution of the first return time to the initial state of a quantum many-body system subject to global projective measurements at stroboscopic times. We show that this distribution can be mapped to a continuation of the canonical partition function of a classical spin chain with noninteracting domains at equilibrium, which is entirely characterized by the Loschmidt amplitude of the quantum many-body system. This allows us to conclude that this probability may decay either algebraically or exponentially at long times, depending on whether the spin chain 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 behavior, which can be tuned by scaling the probing time as a function of $N$. The analysis presented here provides an overarching understanding of many-body quantum first-detection problems in terms of equilibrium thermodynamic phases. Our theoretical predictions are in excellent agreement with exact numerical computations.

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Benjamin Walter, Gabriele Perfetto, Andrea Gambassi. 2023-11-09. Thermodynamic phases in first detected return times of quantum many-body systems. https://doi.org/10.1103/physreva.111.l040202

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