Diffusive entanglement growth in a monitored harmonic chain
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866910355963248640 |
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| author | Young, Thomas Gangardt, Dimitri M. von Keyserlingk, Curt |
| author_facet | Young, Thomas Gangardt, Dimitri M. von Keyserlingk, Curt |
| contents | We study entanglement growth in a harmonic oscillator chain subjected to the weak measurement of observables which have been smeared-out over a length scale $R$. We find that entanglement grows diffusively ($S \sim t^{1/2}$) for a large class of initial Gaussian states provided the measurement scale $R$ is sufficiently large. At late times $t \gtrsim \mathcal{O}(L^{2})$ the entropy relaxes towards an area-law value which we compute exactly. We propose a modified quasi-particle picture which accounts for all of these main features and agrees quantitatively well with our essentially exact numerical results. The quasiparticles are associated with the modes of a non-Hermitian effective Hamiltonian. At small wave-vector $k$, the quasiparticles transport entropy with a finite velocity, but have a lifetime scaling as $1/k^2$; the concurrence of these two conditions leads directly to the observed $t^{1/2}$ growth. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2403_04022 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Diffusive entanglement growth in a monitored harmonic chain Young, Thomas Gangardt, Dimitri M. von Keyserlingk, Curt Quantum Physics We study entanglement growth in a harmonic oscillator chain subjected to the weak measurement of observables which have been smeared-out over a length scale $R$. We find that entanglement grows diffusively ($S \sim t^{1/2}$) for a large class of initial Gaussian states provided the measurement scale $R$ is sufficiently large. At late times $t \gtrsim \mathcal{O}(L^{2})$ the entropy relaxes towards an area-law value which we compute exactly. We propose a modified quasi-particle picture which accounts for all of these main features and agrees quantitatively well with our essentially exact numerical results. The quasiparticles are associated with the modes of a non-Hermitian effective Hamiltonian. At small wave-vector $k$, the quasiparticles transport entropy with a finite velocity, but have a lifetime scaling as $1/k^2$; the concurrence of these two conditions leads directly to the observed $t^{1/2}$ growth. |
| title | Diffusive entanglement growth in a monitored harmonic chain |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2403.04022 |