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  • Letter
  • Open Access

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

Benjamin Walter1, Gabriele Perfetto2,*, and Andrea Gambassi3

  • *Contact author: gabriele.perfetto@uni-tuebingen.de
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Phys. Rev. A 111, L040202 – Published 28 April, 2025

DOI: https://doi.org/10.1103/PhysRevA.111.L040202

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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Phys. Rev. A 111, L040202– Published 28 April, 2025
  • Received 14 March 2024
  • Revised 14 January 2025
  • Accepted 11 March 2025
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