Nonlinear sigma models for monitored dynamics of free fermions

Abstract

We derive field theory descriptions for measurement-induced phase transitions in free fermion systems. We focus on a multi-flavor Majorana chain, undergoing Hamiltonian evolution with continuous monitoring of local fermion parity operators. Using the replica trick, we map the dynamics to the imaginary time evolution of an effective spin chain, and use the number of flavors as a large parameter for a controlled derivation of the effective field theory. This is a nonlinear sigma model for an orthogonal $N\times N$ matrix, in the replica limit $N\to 1$. (On a boundary of the phase diagram, another sigma model with higher symmetry applies.) Together with known results for the renormalization-group beta function, this derivation establishes the existence of stable phases -- nontrivially entangled and disentangled respectively -- in the physically-relevant replica limit $N\to 1$. In the nontrivial phase, an asymptotically exact calculation shows that the bipartite entanglement entropy for a system of size $L$ scales as $(\log L{)}^2$, in contrast to findings in previously-studied models. Varying the relative strength of Hamiltonian evolution and monitoring, as well as a dimerization parameter, the model's phase diagram contains transitions out of the nontrivial phase, which we map to vortex-unbinding transitions in the sigma model, and also contains separate critical points on the measurement-only axis. We highlight the close analogies as well as the differences with the replica approach to Anderson transitions in disordered systems.

Version accepted for publication; added discussion of the phase diagram for more than one flavor. 33 pages, 9 figures

References in corpus (9)

• Anderson Transitions
• A Straightforward Introduction to Continuous Quantum Measurement
• Entanglement Transition in the Projective Transverse Field Ising Model
• Volume-to-Area Law Entanglement Transition in a non-Hermitian Free Fermionic Chain
• Localization in disordered superconducting wires with broken spin-rotation symmetry
• PT-symmetric quantum Liouvillian dynamics
• Entanglement transitions with free fermions
• Density of quasiparticle states for a two-dimensional disordered system: Metallic, insulating, and critical behavior in the class D thermal quantum Hall effect
• Volume-law to area-law entanglement transition in a non-unitary periodic Gaussian circuit

Cited by in corpus (64)

• Theory of free fermions under random projective measurements
• Measurement-induced phase transition for free fermions above one dimension
• Many-body Dynamics in Monitored Atomic Gases Without Post-Selection Barrier
• Entanglement phases, localization and multifractality of monitored free fermions in two dimensions
• Entanglement Dynamics in Monitored Systems and the Role of Quantum Jumps
• Measurement-induced transitions beyond Gaussianity: a single particle description
• Measurement-induced transitions for interacting fermions
• Many-Body Open Quantum Systems
• Monitored fermions with conserved $\mathrm{U}(1)$ charge
• Learnability transitions in monitored quantum dynamics via eavesdropper's classical shadows
• Interactions and integrability in weakly monitored Hamiltonian systems
• Surface codes, quantum circuits, and entanglement phases
• Density and current statistics in boundary-driven monitored fermionic chains
• Boundary transfer matrix spectrum of measurement-induced transitions
• Measurement-induced phase transition in a single-body tight-binding model
• Field theory of monitored, interacting fermion dynamics with charge conservation
• Chaos and magic in the dissipative quantum kicked top
• Enhanced Entanglement in the Measurement-Altered Quantum Ising Chain
• 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
• Entanglement Transition due to particle losses in a monitored fermionic chain
• Entanglement enhancement induced by noise in inhomogeneously monitored systems
• Nonstabilizerness in the unitary and monitored quantum dynamics of XXZ-staggered and SYK models
• Entanglement swapping in critical quantum spin chains
• Measurement-Induced Entanglement Phase Transition in Free Fermion Systems
• Ancilla quantum measurements on interacting chains: Sensitivity of entanglement dynamics to the type and concentration of detectors
• Spacetime picture for entanglement generation in noisy fermion chains
• Universal Stochastic Equations of Monitored Quantum Dynamics
• Measurement-induced Lévy flights of quantum information
• Measurement-induced entanglement and complexity in random constant-depth 2D quantum circuits
• Entanglement dynamics in monitored Kitaev circuits: loop models, symmetry classification, and quantum Lifshitz scaling
• Charge and Spin Sharpening Transitions on Dynamical Quantum Trees
• Exact density profile in a tight-binding chain with dephasing noise
• Controlling measurement-induced phase transitions with tunable detector coupling
• Measurement-Induced Phase Transition in State Estimation of Chaotic Systems and the Directed Polymer
• Topological Modes in Monitored Quantum Dynamics
• Field theory for monitored Brownian SYK clusters
• Measurement-induced phase transitions for free fermions in a quasiperiodic potential
• Topology and Spectrum in Measurement-Induced Phase Transitions
• Random Quantum Circuits with Time-Reversal Symmetry
• Monitored Fluctuating Hydrodynamics
• Measurement-induced phase transition in periodically driven free-fermionic systems
• Entanglement dynamics of monitored noninteracting fermions on graphics processing units
• 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
• Dissipation-Induced Steady States in Topological Superconductors: Mechanisms and Design Principles
• Entanglement behavior and localization properties in monitored fermion systems
• Instability of the engineered dark state in two-band fermions under number-conserving dissipative dynamics
• Computable measures of non-Markovianity for Gaussian free fermion systems
• Symmetry and Topology of Monitored Quantum Dynamics
• Absence of measurement- and unraveling-induced entanglement transitions in continuously monitored one-dimensional free fermions
• Entanglement transition in unitary system-bath dynamics
• Controlled Zeno-Induced Localization of Free Fermions in a Quasiperiodic Chain
• Free-Fermion Measurement-Induced Volume- to Area-Law Entanglement Transition in the Presence of Fermion Interactions
• Entanglement Phase Transition in Chaotic non-Hermitian Systems
• Dephasing-induced Quantum Hall Criticality in the Quantum Anomalous Hall system
• Destruction and recovery of the entanglement entropy of a many-body quantum system after a single measurement
• Entanglement transition and suppression of critical phase of thermofield double state in monitored quantum circuit with unitary $R$ matrix gates
• Replica Keldysh field theory of quantum-jump processes: General formalism and application to imbalanced and inefficient fermion counting
• Asymptotic freedom, lost: Complex conformal field theory in the two-dimensional $O(N>2)$ nonlinear sigma model and its realization in Heisenberg spin chains
• Non-Commutative weak measurements: Entanglement, Symmetry Breaking, and the Role of Readout
• Generation of Volume-Law Entanglement by Local-Measurement-Only Quantum Dynamics