Keldysh Nonlinear Sigma Model for a Free-Fermion Gas under Continuous Measurements

Abstract

Quantum entanglement phase transitions have provided new insights to quantum many-body dynamics. Both disorders and measurements are found to induce similar entanglement transitions. Here, we provide a theoretical framework that unifies these two seemingly disparate concepts and discloses their internal connections. Specifically, we analytically analyze a $d$-dimension free-fermion gas subject to continuous projective measurements. By mapping the Lindblad master equation to the functional Keldysh field theory, we develop an effective theory termed as the time-local Keldysh nonlinear sigma model, which enables us to analytically describe the physics of the monitored system. Our effective theory resembles to that used to describe the disordered fermionic systems. As an application of the effective theory, we study the transport property and obtain a Drude-form conductivity where the elastic scattering time is replaced by the inverse measurement strength. According to these similarities, two different concepts, measurements and disorders, are unified in the same theoretical framework. A numerical verification of our theory and predictions is also provided.

Revised version with the updated main text, reference list, supplementary information including a new numerical caluclation

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Cited by in corpus (26)

• Theory of free fermions under random projective measurements
• Measurement-induced phase transition for free fermions above one dimension
• Entanglement phases, localization and multifractality of monitored free fermions in two dimensions
• Measurement-induced transitions for interacting fermions
• Monitored fermions with conserved $\mathrm{U}(1)$ charge
• Density and current statistics in boundary-driven monitored fermionic chains
• Quantum transport theory for unconventional magnets: Interplay of altermagnetism and p-wave magnetism with superconductivity
• Field theory of non-Hermitian disordered systems
• Generalized Zeno effect and entanglement dynamics induced by fermion counting
• The impact of different unravelings in a monitored system of free fermions
• Localization, fractality, and ergodicity in a monitored qubit
• Ancilla quantum measurements on interacting chains: Sensitivity of entanglement dynamics to the type and concentration of detectors
• Universal Stochastic Equations of Monitored Quantum Dynamics
• Measurement Induced Chirality II: Diffusion and Disorder
• Measurement-induced phase transitions for free fermions in a quasiperiodic potential
• Field theory for monitored Brownian SYK clusters
• Work Statistics and Adiabatic Assumption in Nonequilibrium Many-Body Theory
• Enhanced localization in the prethermal regime of continuously measured many-body localized systems
• Entanglement phases and phase transitions in monitored free fermion system due to localizations
• Symmetry and Topology of Monitored Quantum Dynamics
• Absence of measurement- and unraveling-induced entanglement transitions in continuously monitored one-dimensional free fermions
• Controlled Zeno-Induced Localization of Free Fermions in a Quasiperiodic Chain
• Non-Commutative weak measurements: Entanglement, Symmetry Breaking, and the Role of Readout
• Entanglement Phase Transition in Chaotic non-Hermitian Systems
• Dephasing-induced Quantum Hall Criticality in the Quantum Anomalous Hall system
• Replica Keldysh field theory of quantum-jump processes: General formalism and application to imbalanced and inefficient fermion counting