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This study definitively resolves a debate regarding measurement-induced phase transitions in monitored one-dimensional fermions by demonstrating that previously observed transitions were artifacts of finite-size effects rather than genuine physical phenomena. By scaling simulations to significantly larger system sizes and validating results with nonlinear sigma model analysis, the authors confirm that these systems remain in an area-law phase regardless of disorder strength or monitoring protocols. This clarification is crucial for accurately modeling open quantum dynamics where measurement backaction plays a central role.
No measurement induced phase transition in the entanglement dynamics of monitored non-interacting one-dimensional fermions in a disordered or quasiperiodic potential
arXiv:2605.10758v3 Announce Type: replace Abstract: We show that the entanglement entropy (EE) of one-dimensional (1d) non-interacting fermions with $U(1)$ symmetry in the presence of a disordered or quasi-periodic potential in which the occupation number is being monitored by homodyne or projection protocols is always in an area-law phase so no measurement induced phase transition (MIPT) occurs. The reason for the previously claimed MIPT in these systems was a finite size effect related to the fact that the maximum lattice size $L \simeq 500$ was of the order of the correlation length. By increasing the system size up to $L \simeq 18000$, employing Graphics Processing Units (GPUs), and performing a careful finite-size scaling analysis, we find that the critical monitoring strength is consistent with zero, so no MIPT occurs. For the disordered case, these numerical results are fully supported by an analytical calculation based on mapping the problem onto a nonlinear sigma model (NLSM) that confirms the absence of the MIPT for any monitoring or disorder strength. The effect of disorder is captured by a change of symmetry from BDI to AIII, which results in an enhanced correlation length in the weak disorder limit, and by an effective monitoring strength that increases linearly with disorder.
Abstract:We show that the entanglement entropy (EE) of one-dimensional (1d) non-interacting fermions with $U(1)$ symmetry in the presence of a disordered or quasi-periodic potential in which the occupation number is being monitored by homodyne or projection protocols is always in an area-law phase so no measurement induced phase transition (MIPT) occurs. The reason for the previously claimed MIPT in these systems was a finite size effect related to the fact that the maximum lattice size $L \simeq 500$ was of the order of the correlation length. By increasing the system size up to $L \simeq 18000$, employing Graphics Processing Units (GPUs), and performing a careful finite-size scaling analysis, we find that the critical monitoring strength is consistent with zero, so no MIPT occurs. For the disordered case, these numerical results are fully supported by an analytical calculation based on mapping the problem onto a nonlinear sigma model (NLSM) that confirms the absence of the MIPT for any monitoring or disorder strength. The effect of disorder is captured by a change of symmetry from BDI to AIII, which results in an enhanced correlation length in the weak disorder limit, and by an effective monitoring strength that increases linearly with disorder.
8 pages, 3 figures + Supplemental Materials. Added results for larger sizes and more disorder strength, improved presentation of the analytical results and corrected typos
Quantum Physics (quant-ph); Disordered Systems and Neural Networks (cond-mat.dis-nn)
arXiv:2605.10758 [quant-ph]
(or arXiv:2605.10758v3 [quant-ph] for this version)
From: Antonio M. García-García [view email] [v1] Mon, 11 May 2026 15:55:20 UTC (621 KB) [v2] Tue, 19 May 2026 16:59:47 UTC (621 KB) [v3] Tue, 18 Aug 2026 19:09:42 UTC (631 KB)
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