Berlin 2024 – wissenschaftliches Programm

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TT: Fachverband Tiefe Temperaturen

TT 8: Focus Session: Quantum Interactive Dynamics I (joint session DY/TT)

TT 8.6: Vortrag

Montag, 18. März 2024, 11:30–11:45, A 151

Entanglement phases, localization and multifractality of monitored free fermions in two dimensions — •Karim Chahine and Michael Buchhold — Institut für Theoretische Physik, Universität zu Köln, D-50937 Cologne, Germany

We investigate the entanglement structure and wave function characteristics of continuously monitored free fermions with U(1)-symmetry in 2D. By deriving the fermion replica-Keldysh field theory and a bosonic effective long-wavelength action, we explore the similarities and differences between entanglement phase transitions in 2D monitored fermions and Anderson-type localization transitions in 3D. Using exact numerical simulations, we establish the phenomenology of entanglement transitions in 2D monitored fermions, examining entanglement entropy, mutual information, and inverse participation ratio. At weak monitoring, we observe characteristic L logL entanglement growth and multifractal dimension D_q= 2, resembling a metallic Fermi liquid. At strong monitoring, exponentially localized wave functions lead to saturation, following an area law for entanglement. In between, the critical point exhibits entanglement scaling consistent with emergent conformal invariance and strong multifractality. Our numerical findings align well with mean-field analysis and a one-loop renormalization group treatment of the field theory, shaping the understanding of a monitoring-induced metal-to-insulator transition in entanglement content. This establishes 2D monitored fermions as a unique platform to explore the connection between non-unitary quantum dynamics in D dimensions and quantum statistical mechanics in D+1 dimensions.

Keywords: entanglement entropy; measurement; disorder; free fermions