Quantum dynamics of monitored free fermions: Evolution of quantum correlations and scaling at measurement-induced phase transition
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arXiv
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| Natura: | Preprint |
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2025
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| author | Poboiko, Igor Mirlin, Alexander D. |
| author_facet | Poboiko, Igor Mirlin, Alexander D. |
| contents | We explore, both analytically and numerically, the quantum dynamics of a many-body free-fermion system subjected to local density measurements. We begin by extending the mapping to the nonlinear sigma-model (NLSM) field theory for the case of finite evolution time $T$ and different classes of initial states, which lead to different NLSM boundary conditions. The analytical formalism is then used to study how quantum correlations gradually develop, with increasing $T$, from those determined by the initial state towards their steady-state form. The analytical results are confirmed by numerical simulations for several types of initial states. We further consider the long-time limit, when the system in $d+1$ space-time dimensions becomes quasi-one-dimensional, and analyze the scaling of the ``localization'' time (which is simultaneously the purification time and the charge-sharpening time for this class of problems). The analytical predictions for scaling properties are fully confirmed by numerical simulations in a $d=2$ model around the measurement-induced phase transition. We use this dynamical approach to determine numerically the measurement-induced transition point and the associated correlation-length critical exponent. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_01772 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quantum dynamics of monitored free fermions: Evolution of quantum correlations and scaling at measurement-induced phase transition Poboiko, Igor Mirlin, Alexander D. Disordered Systems and Neural Networks Mesoscale and Nanoscale Physics We explore, both analytically and numerically, the quantum dynamics of a many-body free-fermion system subjected to local density measurements. We begin by extending the mapping to the nonlinear sigma-model (NLSM) field theory for the case of finite evolution time $T$ and different classes of initial states, which lead to different NLSM boundary conditions. The analytical formalism is then used to study how quantum correlations gradually develop, with increasing $T$, from those determined by the initial state towards their steady-state form. The analytical results are confirmed by numerical simulations for several types of initial states. We further consider the long-time limit, when the system in $d+1$ space-time dimensions becomes quasi-one-dimensional, and analyze the scaling of the ``localization'' time (which is simultaneously the purification time and the charge-sharpening time for this class of problems). The analytical predictions for scaling properties are fully confirmed by numerical simulations in a $d=2$ model around the measurement-induced phase transition. We use this dynamical approach to determine numerically the measurement-induced transition point and the associated correlation-length critical exponent. |
| title | Quantum dynamics of monitored free fermions: Evolution of quantum correlations and scaling at measurement-induced phase transition |
| topic | Disordered Systems and Neural Networks Mesoscale and Nanoscale Physics |
| url | https://arxiv.org/abs/2512.01772 |