Keldysh Nonlinear Sigma Model for a Free-Fermion Gas under Continuous Measurements
arXiv:2207.03376 · doi:10.1103/PhysRevResearch.5.033174
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 -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.
arXiv commentRevised version with the updated main text, reference list, supplementary information including a new numerical caluclation
References in corpus (47)
- Holographic Derivation of Entanglement Entropy from AdS/CFT
- Entanglement Entropy and Quantum Field Theory
- Chaos and Quantum Thermalization
- Many body localization and thermalization in quantum statistical mechanics
- Metal-insulator transition in a weakly interacting many-electron system with localized single-particle states
- Localization of interacting fermions at high temperature
- Many-body localization, thermalization, and entanglement
- Observation of many-body localization of interacting fermions in a quasi-random optical lattice
- The many-body localization phase transition
- Many-body localization edge in the random-field Heisenberg chain
- Interacting electrons in disordered wires: Anderson localization and low-temperature transport
- Quantum entanglement in condensed matter systems
- Measurement-Induced Phase Transitions in the Dynamics of Entanglement
- Quantum Zeno Effect and the Many-body Entanglement Transition
- Quantum Entanglement Growth Under Random Unitary Dynamics
- Many-body localization in a disordered quantum Ising chain
- Measurement-driven entanglement transition in hybrid quantum circuits
- A Straightforward Introduction to Continuous Quantum Measurement
- Keldysh Field Theory for Driven Open Quantum Systems
- Area laws in a many-body localized state and its implications for topological order
- Measurement-induced criticality in random quantum circuits
- Quantum Error Correction in Scrambling Dynamics and Measurement-Induced Phase Transition
- Dynamical purification phase transitions induced by quantum measurements
- Theory of the many-body localization transition in one dimensional systems
- Entanglement transition in a monitored free fermion chain -- from extended criticality to area law
- Entanglement in a fermion chain under continuous monitoring
- Universal properties of many-body delocalization transitions
- Effective Theory for the Measurement-Induced Phase Transition of Dirac Fermions
- Electron--electron Interactions in Disordered Metals: Keldysh Formalism
- Critical Properties of the Many-Body Localization Transition
- Measurement-induced quantum criticality under continuous monitoring
- Low-frequency conductivity in many-body localized systems
- Exact solution for a diffusive nonequilibrium steady state of an open quantum chain
- Entanglement and charge-sharpening transitions in U(1) symmetric monitored quantum circuits
- Universality of entanglement transitions from stroboscopic to continuous measurements
- Emergent conformal symmetry in non-unitary random dynamics of free fermions
- Quantum butterfly effect in weakly interacting diffusive metals
- Measurement-induced transitions of the entanglement scaling law in ultracold gases with controllable dissipation
- Possible experimental manifestations of the many-body localization
- Dephasing-induced diffusive transport in anisotropic Heisenberg model
- Bath-induced Zeno localization in driven many-body quantum systems
- Generalized quantum measurements with matrix product states: Entanglement phase transition and clusterization
- Nonlinear sigma model approach to many-body quantum chaos: Regularized and unregularized out-of-time-ordered correlators
- Exact description of quantum stochastic models as quantum resistors
- Intrinsic dissipative Floquet superconductors beyond mean-field theory
- Semi-classical theory of quantum stochastic resistors
- Diffusion and Thermalization in a Boundary-Driven Dephasing Model
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- 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 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