Theory of measurement-induced phase transitions

• Applicant: Professor Dr. Alexander Mirlin
• Subject Area: Theoretical Condensed Matter Physics
• Term: since 2025
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 553096561

The problem of influence of quantum measurements on entanglement and, in particular, of measurement-induced entanglement phase transitions has recently attracted much attention. This problem belongs to a broad field of research on dynamics of open systems in contact with environment, with the measurement apparatus being a specific realization of the environment. A great interest in this area of research is motivated by current developments in quantum information processing. Very recently, the PI and collaborators developed a field theory of free fermions under random measurements and verified some of its predictions by numerical simulations on 1D and 2D models, demonstrating important analogies and connections to the field of Anderson localization. These preliminary results pave the way for major advances in investigations of measurement-induced phases and phase transitions and serve as a key starting point for the present project. The overall goal of this project is to develop a theory of measurement-induced phase transitions based on the non-linear-sigma-model (NLSM) field-theoretical approach supported by numerical simulations. The Objectives of the project are structured in six interrelated Tasks. Task 1 will address the measurement-induced transition in a free-fermion system with particle-number conservation. The aim is to explore distributions of key observables at and around the transition, including statistics of density fluctuations and of mutual information as well as multifractal properties. Task 2 will extend the investigation of the transition to other symmetry classes and to crossovers between symmetry classes. Task 3 aims at exploring the role of topology in measurement-induced transitions. Task 4 will extend the theory of measurement-induced phase transitions on models with interaction. The objective of Task 5 is to incorporate static disorder in the problem, first in the absence of interaction and then in combination with interaction, which is expected to lead to very rich physics. Finally, Task 6 will extend the analysis to finite-time dynamical properties and in particular explore measurement-induced evolution of mixed states. Implementation of this proposal will be a major advance in our understanding of measurement-induced transitions, including such key facets as spatial dimensionalities, symmetries, topologies, interaction, disorder, and dynamical scaling. In this way, the project will shape the field of ``localization and mesoscopics'' of quantum information, which is expected to have a large impact on future research.

• DFG Programme: Research Grants