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arXiv:2311.13011 · Physical review. B./Physical review. B

Ancilla quantum measurements on interacting chains: Sensitivity of entanglement dynamics to the type and concentration of detectors

Elmer V. H. Doggen, I. V. Gornyi, A. D. Mirlin

Published Jun 11, 2024• 9 citations
arXivHTMLPDF

Abstract

We consider a quantum many-body lattice system that is coupled to ancillary degrees of freedom (``detectors''), which are periodically measured by means of strong projective measurements. The concentration ${\ensuremath{\rho}}_{a}$ of ancillae and their coupling $M$ to the main system are considered as parameters. We explore the dynamics of density and of entanglement entropy in the chain, for various values of ${\ensuremath{\rho}}_{a}$ and $M$ for two models of the detector-chain interaction that couple the local density in the chain to a detector degree of freedom. It is found that, for the density-density (${S}_{z}{s}_{z}$-type in spin language) coupling, the critical values ${M}_{c}$ for the measurement-induced entanglement transition depends sensitively on ${\ensuremath{\rho}}_{a}$. Moreover, our results indicate that for a sufficiently small ${\ensuremath{\rho}}_{a}$ the transition in this model disappears; i.e., a finite density of detectors is needed to reach a disentangling phase. The behavior is qualitatively different for the second model, with density-hopping (${S}_{z}{s}_{x}$-type) coupling. Specifically, the dynamics is much less sensitive to the concentration ${\ensuremath{\rho}}_{a}$ of detectors than in the first model. Furthermore, the dependence of entanglement on the coupling strength $M$ is strongly nonmonotonic, indicating reentrance of the entangling phase at large $M$.

DOI
10.1103/physrevb.109.224203

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We consider a quantum many-body lattice system that is coupled to ancillary degrees of freedom (``detectors''), which are periodically measured by means of strong projective measurements. The concentration \ensuremathρa{\ensuremath{\rho}}_{a}\ensuremathρa​ of ancillae and their coupling MMM to the main system are considered as parameters. We explore the dynamics of density and of entanglement entropy in the chain, for various values of \ensuremathρa{\ensuremath{\rho}}_{a}\ensuremathρa​ and MMM for two models of the detector-chain interaction that couple the local density in the chain to a detector degree of freedom. It is found that, for the density-density (Szsz{S}_{z}{s}_{z}Sz​sz​-type in spin language) coupling, the critical values Mc{M}_{c}Mc​ for the measurement-induced entanglement transition depends sensitively on \ensuremathρa{\ensuremath{\rho}}_{a}\ensuremathρa​. Moreover, our results indicate that for a sufficiently small \ensuremathρa{\ensuremath{\rho}}_{a}\ensuremathρa​ the transition in this model disappears; i.e., a finite density of detectors is needed to reach a disentangling phase. The behavior is qualitatively different for the second model, with density-hopping (Szsx{S}_{z}{s}_{x}Sz​sx​-type) coupling. Specifically, the dynamics is much less sensitive to the concentration \ensuremathρa{\ensuremath{\rho}}_{a}\ensuremathρa​ of detectors than in the first model. Furthermore, the dependence of entanglement on the coupling strength MMM is strongly nonmonotonic, indicating reentrance of the entangling phase at large MMM.
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