Free-Fermion Measurement-Induced Volume- to Area-Law Entanglement Transition in the Presence of Fermion Interactions

Abstract

At a generic volume- to area-law entanglement transition in a many-body system, quantum chaos is arrested. We argue that this tends to imply the vanishing of a certain "mass" term in the field theory of the measurement-induced phase transition (MIPT) for monitored, interacting fermions. To explore this idea, we consider the MIPT with no conserved quantities that describes 1D monitored, interacting Majorana fermions in class DIII. This is the most general problem of interacting fermions with weak fermion parity measurements. Without interactions, it is known that a noninteracting MIPT separates the area-law phase from a log-enhanced "thermal metal" phase at sufficiently weak monitoring. We conjecture that the MIPT with interactions is the same as the noninteracting one in this case; the volume-law phase arises through the dangerously irrelevant mass. The physical picture is that the mass represents a local Fermi's golden rule interparticle scattering rate density that is tantamount to the entangling rate density. The latter must vanish continuously at a continuous MIPT. On the other hand, the field theory capturing the MIPT for monitored fermions with additional continuous symmetries is expected to be different, because the interactions introduce additional terms associated to conserved Noether currents. We propose numerical tests of our conjecture. In addition, we analytically identify a candidate noninteracting critical point representing the MIPT, using a controlled $\epsilon$-expansion.

arXiv comment9+5 pages, 2 figures; v2: 14 pages, 3 figures, published version

References in corpus (62)

• Classification of topological insulators and superconductors in three spatial dimensions
• Topological insulators and superconductors: ten-fold way and dimensional hierarchy
• Anderson Transitions
• Metal-insulator transition in a weakly interacting many-electron system with localized single-particle states
• Measurement-Induced Phase Transitions in the Dynamics of Entanglement
• Quantum Zeno Effect and the Many-body Entanglement Transition
• Quasiparticle Lifetime in a Finite System: A Non--Perturbative Approach
• Riemannian symmetric superspaces and their origin in random matrix theory
• Measurement-driven entanglement transition in hybrid quantum circuits
• Keldysh Field Theory for Driven Open Quantum Systems
• 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
• Quantum Error Correction in Scrambling Dynamics and Measurement-Induced Phase Transition
• Dynamical purification phase transitions induced by quantum measurements
• Critical properties of the measurement-induced transition in random quantum circuits
• Entanglement transition in a monitored free fermion chain -- from extended criticality to area law
• Entanglement in a fermion chain under continuous monitoring
• Scalable probes of measurement-induced criticality
• Emergent statistical mechanics of entanglement in random unitary circuits
• Measurement-induced topological entanglement transitions in symmetric random quantum circuits
• Entanglement Transitions from Holographic Random Tensor Networks
• Measurement and entanglement phase transitions in all-to-all quantum circuits, on quantum trees, and in Landau-Ginsburg theory
• Measurement-induced quantum criticality under continuous monitoring
• Measurement-induced criticality in (2+1)-d hybrid quantum circuits
• Topology, Delocalization via Average Symmetry and the Symplectic Anderson Transition
• Conformal invariance and quantum non-locality in critical hybrid circuits
• Entanglement and charge-sharpening transitions in U(1) symmetric monitored quantum circuits
• Entanglement Transition in the Projective Transverse Field Ising Model
• Operator scaling dimensions and multifractality at measurement-induced transitions
• Entanglement and dynamics of diffusion-annihilation processes with Majorana defects
• Correcting coherent errors with surface codes
• Theory of free fermions under random projective measurements
• Random-bond Ising model in two dimensions, the Nishimori line, and supersymmetry
• Entanglement Negativity at Measurement-Induced Criticality
• Nonuniversal Entanglement Level Statistics in Projection-driven Quantum Circuits
• How Dynamical Quantum Memories Forget
• Cross Entropy Benchmark for Measurement-Induced Phase Transitions
• Nonlinear sigma models for monitored dynamics of free fermions
• Measurement-induced phase transition for free fermions above one dimension
• Entanglement Domain Walls in Monitored Quantum Circuits and the Directed Polymer in a Random Environment
• Transitions in the learnability of global charges from local measurements
• Entanglement transitions with free fermions
• Critical phase and spin sharpening in SU(2)-symmetric monitored quantum circuits
• Triviality of quantum trajectories close to a directed percolation transition
• Coherent error threshold for surface codes from Majorana delocalization
• Entanglement phases, localization and multifractality of monitored free fermions in two dimensions
• Measurement-induced transitions beyond Gaussianity: a single particle description
• Measurement-induced transitions for interacting fermions
• Statistical mechanics model for Clifford random tensor networks and monitored quantum circuits
• Monitored fermions with conserved $\mathrm{U}(1)$ charge
• Response theory of the ergodic many-body delocalized phase: Keldysh Finkel'stein sigma models and the 10-fold way
• Surface codes, quantum circuits, and entanglement phases
• Boundary transfer matrix spectrum of measurement-induced transitions
• Renormalization group for measurement and entanglement phase transitions
• Field theory of monitored, interacting fermion dynamics with charge conservation
• Dephasing catastrophe in $4-\epsilon$ dimensions: A possible instability of the ergodic (many-body-delocalized) phase
• Random insights into the complexity of two-dimensional tensor network calculations
• Flow to Nishimori universality in weakly monitored quantum circuits with qubit loss
• Field theory for monitored Brownian SYK clusters
• Free-Fermion Dynamics with Measurements: Topological Classification and Adaptive Preparation of Topological States