Entanglement phases, localization and multifractality of monitored free fermions in two dimensions

Abstract

We investigate the entanglement structure and wave function characteristics of continuously monitored free fermions with U$(1)$-symmetry in two spatial dimensions (2D). By deriving the exact fermion replica-quantum master equation, we line out two approaches: (i) a nonlinear sigma model analogous to disordered free fermions, resulting in an SU$(R)$-symmetric field theory of symmetry class AIII in (2+1) space-time dimensions, or (ii) for bipartite lattices, third quantization leading to a non-Hermitian SU$(2R)$-symmetric Hubbard model. Using exact numerical simulations, we explore the phenomenology of the entanglement transition in 2D monitored fermions, examining entanglement entropy and wave function inverse participation ratio. At weak monitoring, we observe characteristic $L\log L$ entanglement growth and multifractal dimension $D_q=2$, resembling a metallic Fermi liquid. Under strong monitoring, wave functions localize and the entanglement saturates towards an area law. Between these regimes, we identify a high-symmetry point exhibiting both entanglement growth indicative of emergent conformal invariance and maximal multifractal behavior. While this multifractal behavior aligns with the nonlinear sigma model of the Anderson transition, the emergent conformal invariance is an unexpected feature not typically associated with Anderson localization. These discoveries add a new dimension to the study of 2D monitored fermions and underscore the need to further explore the connection between non-unitary quantum dynamics in $D$ dimensions and quantum statistical mechanics in $D+1$ dimensions.

References in corpus (54)

• Anderson Transitions
• Area laws in quantum systems: mutual information and correlations
• Third quantization: a general method to solve master equations for quadratic open Fermi systems
• Random Quantum Circuits
• Critical properties of the measurement-induced transition in random quantum circuits
• Quantum Noise as an Entanglement Meter
• Measurement-Induced Entanglement Transitions in the Quantum Ising Chain: From Infinite to Zero Clicks
• Observation of measurement-induced quantum phases in a trapped-ion quantum computer
• Measurement and entanglement phase transitions in all-to-all quantum circuits, on quantum trees, and in Landau-Ginsburg theory
• Measurement-induced dark state phase transitions in long-ranged fermion systems
• Entanglement Transitions from Stochastic Resetting of Non-Hermitian Quasiparticles
• Entanglement and purification transitions in non-Hermitian quantum mechanics
• SYK meets non-Hermiticity II: measurement-induced phase transition
• Entanglement and charge-sharpening transitions in U(1) symmetric monitored quantum circuits
• Operator scaling dimensions and multifractality at measurement-induced transitions
• Fate of measurement-induced phase transition in long-range interactions
• Symmetry enriched phases of quantum circuits
• Growth of entanglement entropy under local projective measurements
• Fractal, logarithmic and volume-law entangled non-thermal steady states via spacetime duality
• Universal behavior beyond multifractality of wave-functions at measurement--induced phase transitions
• Theory of free fermions under random projective measurements
• Nishimori's cat: stable long-range entanglement from finite-depth unitaries and weak measurements
• Topological transitions with continuously monitored free fermions
• Nonlinear sigma models for monitored dynamics of free fermions
• Monitored Open Fermion Dynamics: Exploring the Interplay of Measurement, Decoherence, and Free Hamiltonian Evolution
• Measurement-induced phase transition for free fermions above one dimension
• Controlling entanglement at absorbing state phase transitions in random circuits
• Measuring nonstabilizerness via multifractal flatness
• Disordered monitored free fermions
• Measurement-induced criticality as a data-structure transition
• Dynamical phases and quantum correlations in an emitter-waveguide system with feedback
• Full counting statistics as probe of measurement-induced transitions in the quantum Ising chain
• Generalized quantum measurements with matrix product states: Entanglement phase transition and clusterization
• Continuous Gaussian Measurements of the Free Boson CFT: A model for Exactly Solvable and Detectable Measurement-Induced Dynamics
• Topology, criticality, and dynamically generated qubits in a stochastic measurement-only Kitaev model
• Charge fluctuation and charge-resolved entanglement in a monitored quantum circuit with $U(1)$ symmetry
• Purification Timescales in Monitored Fermions
• Critical phase and spin sharpening in SU(2)-symmetric monitored quantum circuits
• Dynamics of measured many-body quantum chaotic systems
• Entangled multiplets and unusual spreading of quantum correlations in a continuously monitored tight-binding chain
• Topological order and entanglement dynamics in the measurement-only XZZX quantum code
• Triviality of quantum trajectories close to a directed percolation transition
• Localization properties in disordered quantum many-body dynamics under continuous measurement
• Entanglement and Absorbing-State Transitions in Interactive Quantum Dynamics
• Majorana Loop Models for Measurement-Only Quantum Circuits
• Diagnosing entanglement dynamics in noisy and disordered spin chains via the measurement-induced steady-state entanglement transition
• Keldysh Nonlinear Sigma Model for a Free-Fermion Gas under Continuous Measurements
• Measurements on an Anderson Chain
• Interactions and integrability in weakly monitored Hamiltonian systems
• Surface codes, quantum circuits, and entanglement phases
• Detecting and stabilizing measurement-induced symmetry-protected topological phases in generalized cluster models
• Measurement induced transitions in non-Markovian free fermion ladders
• Density and current statistics in boundary-driven monitored fermionic chains
• Measurement-induced phase transition in a single-body tight-binding model

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• Entanglement dynamics in monitored Kitaev circuits: loop models, symmetry classification, and quantum Lifshitz scaling
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• Topological Modes in Monitored Quantum Dynamics
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• Multifractality in monitored single-particle dynamics
• Measurement-induced phase transition in periodically driven free-fermionic systems
• Mesoscopic Fluctuations and Multifractality at and across Measurement-Induced Phase Transition
• Entanglement dynamics of monitored noninteracting fermions on graphics processing units
• Entanglement behavior and localization properties in monitored fermion systems
• Quantum dynamics of monitored free fermions: Evolution of quantum correlations and scaling at measurement-induced phase transition
• Free-Fermion Dynamics with Measurements: Topological Classification and Adaptive Preparation of Topological States
• Entanglement transition in unitary system-bath dynamics
• Absence of measurement- and unraveling-induced entanglement transitions in continuously monitored one-dimensional free fermions
• Symmetry and Topology of Monitored Quantum Dynamics
• Generation of Volume-Law Entanglement by Local-Measurement-Only Quantum Dynamics
• Dephasing-induced Quantum Hall Criticality in the Quantum Anomalous Hall system
• Free-Fermion Measurement-Induced Volume- to Area-Law Entanglement Transition in the Presence of Fermion Interactions
• Replica Keldysh field theory of quantum-jump processes: General formalism and application to imbalanced and inefficient fermion counting
• Destruction and recovery of the entanglement entropy of a many-body quantum system after a single measurement