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DY: Fachverband Dynamik und Statistische Physik

DY 35: Poster: Quantum Dynamics and Many-body Systems

DY 35.23: Poster

Wednesday, March 20, 2024, 15:00–18:00, Poster D

Entanglement spectrum and multifractality in 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. Using exact numerical simulations, we establish the phenomenology of the entanglement transition and explore the similarities and differences with Anderson-type localization transitions. At weak monitoring, we observe characteristic L logL entanglement growth and multifractal dimension D_q= 2, resembling a metallic Fermi liquid. Furthermore, excellent agreement is found with a Wigner-Dyson distribution for the entanglement spectrum statistics. At strong monitoring, exponentially localized wave functions lead to saturation, following an area law for entanglement and a Poissonian distribution for the entanglement spectrum is seen. In between, the critical point exhibits entanglement scaling consistent with emergent conformal invariance and strong multifractality. Furthermore, we numerically reveal a close link between the multifractal exponent D_q and the purification decay rate and find another witness of multifractality in the spectral form factor. Our results shape 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; multifractality