Multifractality in monitored single-particle dynamics
arXiv:2406.02386 · doi:10.1103/PhysRevResearch.6.043049
Abstract
We study multifractal properties in time evolution of a single particle subject to repeated measurements. For quantum systems, we consider circuit models consisting of local unitary gates and local projective measurements. For classical systems, we consider models for estimating the trajectory of a particle evolved under local transition processes by partially measuring particle occupations. In both cases, multifractal behaviors appear in the ensemble of wave functions or probability distributions conditioned on measurement outcomes after a sufficiently long time. While the nature of particle transport (diffusive or ballistic) qualitatively affects the multifractal properties, they are even quantitatively robust to the measurement rate or specific protocols. On the other hand, multifractality is generically lost by generalized measurements allowing erroneous outcomes or by postselection of the outcomes with no particle detection. We demonstrate these properties by numerical simulations and also propose several simplified models, which allow us to analytically obtain multifractal properties in the monitored single-particle systems.
19 pages, 20 figures, v3: References added. Published version
References in corpus (60)
- Anderson Transitions
- Diffusion with Stochastic Resetting
- Measurement-Induced Phase Transitions in the Dynamics of Entanglement
- Quantum Zeno Effect and the Many-body Entanglement Transition
- Stochastic Resetting and Applications
- Measurement-driven entanglement transition in hybrid quantum circuits
- Theory of the phase transition in random unitary circuits with measurements
- Measurement-induced criticality in random quantum circuits
- Random Quantum Circuits
- Unitary-projective entanglement dynamics
- Dynamical purification phase transitions induced by quantum measurements
- Entanglement transition in a monitored free fermion chain -- from extended criticality to area law
- Entanglement in a fermion chain under continuous monitoring
- Measurement-Induced Entanglement Transitions in the Quantum Ising Chain: From Infinite to Zero Clicks
- Entanglement transition from variable-strength weak measurements
- Fluctuations of the inverse participation ratio at the Anderson transition
- Multifractality and critical fluctuations at the Anderson transition
- Multifractal finite-size-scaling and universality at the Anderson transition
- Exact relations between multifractal exponents at the Anderson transition
- Entanglement Transitions from Stochastic Resetting of Non-Hermitian Quasiparticles
- Entanglement and charge-sharpening transitions in U(1) symmetric monitored quantum circuits
- Correlation-induced localization
- Critical parameters from generalised multifractal analysis at the Anderson transition
- Phase diagram of a non-Abelian Aubry-André-Harper model with -wave superfluidity
- Growth of entanglement entropy under local projective measurements
- Observation of multifractality in Anderson localization of ultrasound
- Universal behavior beyond multifractality of wave-functions at measurement--induced phase transitions
- Many-Body Quantum Zeno Effect and Measurement-Induced Subradiance Transition
- Theory of free fermions under random projective measurements
- Localization transition induced by learning in random searches
- Multifractality of wavefunctions at the quantum Hall transition revisited
- Multifractality at the quantum Hall transition: Beyond the parabolic paradigm
- How Dynamical Quantum Memories Forget
- Multifractal analysis of the metal-insulator transition in the 3D Anderson model I: Symmetry relation under typical averaging
- Realization and detection of non-ergodic critical phases in optical Raman lattice
- Conformal invariance, multifractality, and finite-size scaling at Anderson localization transitions in two dimensions
- Multifractal analysis of the metal-insulator transition in the 3D Anderson model II: Symmetry relation under ensemble averaging
- Critical phase dualities in 1D exactly-solvable quasiperiodic models
- Boundary multifractality at the integer quantum Hall plateau transition: implications for the critical theory
- Disordered monitored free fermions
- Multifractality without fine-tuning in a Floquet quasiperiodic chain
- The integer quantum Hall plateau transition is a current algebra after all
- Quantum Levy flights and multifractality of dipolar excitations in a random system
- Surface criticality and multifractality at localization transitions
- Magnetic properties of Sr_2Fe_1+xMo_1-xO_6 with -1 <= x <= 0.25
- Charge fluctuation and charge-resolved entanglement in a monitored quantum circuit with symmetry
- Classification and symmetry properties of scaling dimensions at Anderson transitions
- Symmetries of multifractal spectra and field theories of Anderson localization
- Entanglement phases, localization and multifractality of monitored free fermions in two dimensions
- Spectral statistics, finite-size scaling and multifractal analysis of quasiperiodic chain with p-wave pairing
- Anderson-like localization transition of random walks with resetting
- Edge and bulk localization of Floquet topological superconductors
- Anomalous multifractality in quantum chains with strongly correlated disorder
- Measurements on an Anderson Chain
- KPZ physics and phase transition in a classical single random walker under continuous measurement
- Measurement-induced phase transition in a single-body tight-binding model
- Charge and Entanglement Criticality in a U(1)-Symmetric Hybrid Circuit of Qubits
- Symmetry Violation of Quantum Multifractality: Gaussian fluctuations versus Algebraic Localization
- Conformal Invariance and Multifractality at Anderson Transitions in Arbitrary Dimensions
- Extended critical phase in quasiperiodic quantum Hall systems