Thermodynamic phases in first detected return times of quantum many-body systems
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866916715909087232 |
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| author | Walter, Benjamin Perfetto, Gabriele Gambassi, Andrea |
| author_facet | Walter, Benjamin Perfetto, Gabriele Gambassi, Andrea |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_05585 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Thermodynamic phases in first detected return times of quantum many-body systems Walter, Benjamin Perfetto, Gabriele Gambassi, Andrea Statistical Mechanics Quantum Physics 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. |
| title | Thermodynamic phases in first detected return times of quantum many-body systems |
| topic | Statistical Mechanics Quantum Physics |
| url | https://arxiv.org/abs/2311.05585 |