Larger Simulations Confirm No New Quantum Phase Transition Emerges

A thorough investigation into the entanglement dynamics of one-dimensional non-interacting fermions within disordered or quasiperiodic potentials reveals no measurement-induced phase transition. Can Yin at Karlsruhe Institute of Technology, and colleagues in collaboration with the Institute for Quantum Materials and Technologies, Shanghai Jiao Tong University, China and Tsung-Dao Lee Institute, demonstrate that earlier reports of such a transition resulted from finite size effects. Extensive numerical simulations, utilising Graphics Processing Units and systems up to a size of 18000, alongside analytical calculations mapping the problem onto a nonlinear sigma model, show that the critical monitoring strength remains consistent with zero. This confirms an area-law phase prevails irrespective of monitoring or disorder strength. The findings clarify the behaviour of monitored fermionic systems and highlight the vital role of careful finite size scaling analysis in identifying genuine phase transitions.

GPU acceleration unlocks larger quantum system simulations revealing extended correlation lengths

Employing Graphics Processing Units (GPUs) overcame a longstanding limitation in simulating quantum systems. Calculations were previously restricted to around 500 lattice sites, hindering accurate observation of subtle quantum behaviours. GPUs massively accelerate the intensive numerical simulations required to model the entanglement of many interacting particles, allowing systems to scale up to 18000 lattice sites, a sharp leap in computational power. This increased scale proved key because the distance over which quantum properties remain linked, known as the correlation length, was comparable to the size of earlier simulations, masking the true underlying physics. Quantum systems were simulated using Graphics Processing Units, extending calculations to a maximum of 18000 lattice sites, a significant increase from the previous limit of around 500. The correlation length, defining the distance over which quantum entanglement persists, was previously comparable to simulation size, obscuring underlying physics, making this increase essential.

Large-scale entanglement simulations rule out measurement-induced phase transitions in

Entanglement measures now extend to systems of 18000 lattice sites, a substantial increase from the previous limit of approximately 500 sites. This leap in scale was essential because the correlation length, the distance over which quantum properties remain linked, was previously comparable to simulation size, obscuring true behaviour. By exceeding this threshold, the absence of a measurement-induced phase transition (MIPT) in one-dimensional non-interacting fermions has been definitively demonstrated, even when subjected to disorder or a quasi-periodic potential.

Analytical calculations, mapping the problem onto a nonlinear sigma model, corroborate these numerical findings and confirm an area-law phase prevails regardless of monitoring or disorder strength. Simulations encompassed up to 18000 lattice sites, exceeding previous limits of around 500, to accurately model quantum entanglement. This increase in scale was key because the correlation length, defining the reach of linked quantum properties, had previously been comparable to the simulation size, obscuring genuine system behaviour. Detailed analysis revealed the critical monitoring strength remains consistent with zero, definitively ruling out a measurement-induced phase transition (MIPT) in one-dimensional non-interacting fermions, even with both disorder and quasi-periodic potentials applied. Supporting this, analytical calculations using a nonlinear sigma model (NLSM) confirmed an area-law phase prevails regardless of measurement intensity or the strength of disorder, and the correlation length increases with disorder strength in weakly disordered systems.

Finite system sizes masked true quantum behaviour in monitoring experiments

Scientists have long sought to understand how continuous monitoring affects fragile quantum states, a vital step towards building stable quantum computers. Recent debate has centred on whether this monitoring can induce a fundamental shift in the system’s behaviour, known as a measurement-induced phase transition. This work directly challenges those claims, revealing that previous observations likely arose from inadequately sized simulations. The correlation length, defining the distance over which quantum properties remain linked, was comparable to the system size.

However, these findings do not invalidate earlier work entirely. They demonstrate that previous simulations were too small to accurately capture the system’s behaviour. Establishing the true scale of correlation lengths, the distance over which quantum properties are linked, required sharply larger simulations utilising advanced computing power. This detailed analysis clarifies that the observed effects were finite-size effects, not a fundamental change in quantum state induced by monitoring, highlighting a matter of scale rather than a new phenomenon.

Simulations were limited by their size, failing to capture the full extent of quantum entanglement. Powerful computing revealed these effects were finite-size, not a fundamental shift in quantum behaviour. The correlation length, how far quantum properties remain connected, was simply very large. Confirming the stability of monitored quantum systems, simulations now demonstrate one-dimensional fermions retain an area-law phase even with both disorder and quasi-periodic potentials, signifying that entanglement grows proportionally to the system’s surface, indicating stability. Extending calculations to 18000 lattice sites, utilising Graphics Processing Units, revealed the critical monitoring strength remained at zero, definitively ruling out a previously suggested measurement-induced phase transition, and demonstrating earlier results were limited by inadequate system sizes.

The research demonstrated that one-dimensional fermions do not undergo a measurement-induced phase transition when monitored by homodyne or quantum jump protocols, even in the presence of disorder or quasi-periodic potentials. Previous claims of such a transition were found to be due to finite-size effects in simulations, where the system size was comparable to the correlation length. By increasing the system size to up to 18000 lattice sites and employing GPU computing, researchers confirmed the critical monitoring strength is consistent with zero. These findings clarify the behaviour of monitored quantum systems and highlight the importance of accurately scaling simulations to avoid misinterpreting finite-size artefacts.