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

TL;DR

This paper explores the distribution of first return times in quantum many-body systems under measurements, revealing phase-dependent decay behaviors linked to classical spin chain thermodynamics.

Contribution

It establishes a novel mapping between quantum first return time distributions and classical thermodynamic phases, providing a unified framework for understanding many-body quantum detection.

Findings

Return time distribution can decay algebraically or exponentially.

Phase behavior can be tuned by probing time scaling.

Theoretical predictions match numerical simulations.

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.