Controlled Zeno-Induced Localization of Free Fermions in a Quasiperiodic Chain
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| Format: | Preprint |
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2026
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| _version_ | 1866918501422202880 |
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| author | Singha, Pinaki Roy, Nilanjan Szyniszewski, Marcin Sharma, Auditya |
| author_facet | Singha, Pinaki Roy, Nilanjan Szyniszewski, Marcin Sharma, Auditya |
| contents | We investigate measurement-induced localization in a continuously monitored one-dimensional Aubry--André--Harper model, focusing on the quantum Zeno regime in which the measurements dominate coherent dynamics. The presence of a quasiperiodic potential renders the problem analytically tractable and enables a controlled study of the interplay between monitoring and disorder. We develop an analytical description based on an instantaneous Schrödinger equation with a measurement-induced effective potential constructed self-consistently from individual quantum trajectories, without relying on postselection. In the quantum Zeno regime, an emergent dominant energy scale reduces the problem to a transfer-matrix formulation of an effective non-Hermitian Hamiltonian, which allows direct computation of the Lyapunov exponent. Complementarily, we extract the localization length numerically from long-time steady-state quantum state diffusion trajectories by reconstructing the intrinsic localized single-particle wave functions and analyzing their spatial decay. These numerical results show quantitative agreement with the effective theory predictions, with controlled corrections of order $J^2/[λ^2+(γ/2)^2]$ (where $J$ is the hopping amplitude, $γ$ the measurement strength, and $λ$ the quasiperiodic potential). Our results underscore the connection between the effective non-Hermitian description and the stochastic monitored dynamics, showing the interplay between Zeno-like localization, coherent hopping, and quasiperiodic-disorder-induced localization, while also laying the groundwork for understanding and exploiting measurement-induced localization as a tool for quantum control and state preparation. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2602_12340 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Controlled Zeno-Induced Localization of Free Fermions in a Quasiperiodic Chain Singha, Pinaki Roy, Nilanjan Szyniszewski, Marcin Sharma, Auditya Statistical Mechanics Disordered Systems and Neural Networks Quantum Physics We investigate measurement-induced localization in a continuously monitored one-dimensional Aubry--André--Harper model, focusing on the quantum Zeno regime in which the measurements dominate coherent dynamics. The presence of a quasiperiodic potential renders the problem analytically tractable and enables a controlled study of the interplay between monitoring and disorder. We develop an analytical description based on an instantaneous Schrödinger equation with a measurement-induced effective potential constructed self-consistently from individual quantum trajectories, without relying on postselection. In the quantum Zeno regime, an emergent dominant energy scale reduces the problem to a transfer-matrix formulation of an effective non-Hermitian Hamiltonian, which allows direct computation of the Lyapunov exponent. Complementarily, we extract the localization length numerically from long-time steady-state quantum state diffusion trajectories by reconstructing the intrinsic localized single-particle wave functions and analyzing their spatial decay. These numerical results show quantitative agreement with the effective theory predictions, with controlled corrections of order $J^2/[λ^2+(γ/2)^2]$ (where $J$ is the hopping amplitude, $γ$ the measurement strength, and $λ$ the quasiperiodic potential). Our results underscore the connection between the effective non-Hermitian description and the stochastic monitored dynamics, showing the interplay between Zeno-like localization, coherent hopping, and quasiperiodic-disorder-induced localization, while also laying the groundwork for understanding and exploiting measurement-induced localization as a tool for quantum control and state preparation. |
| title | Controlled Zeno-Induced Localization of Free Fermions in a Quasiperiodic Chain |
| topic | Statistical Mechanics Disordered Systems and Neural Networks Quantum Physics |
| url | https://arxiv.org/abs/2602.12340 |