arXiv 2403.040222024-03-06quant-ph

受监控谐振链中的扩散式纠缠增长

Diffusive entanglement growth in a monitored harmonic chain

Thomas Young, Dimitri M. Gangardt, Curt von Keyserlingk

AI总结：

该研究针对经受展宽弱测量的谐振子链，发现大测量尺度下纠缠呈扩散式增长，提出与非厄米有效哈密顿量模式相关的修正准粒子图像，定量吻合数值结果并解释了增长机制。

摘要：

我们研究了经受可观测弱测量的谐振子链中的纠缠增长，这些可观测量在长度尺度$R$上被展宽。我们发现，只要测量尺度$R$足够大，对于一大类初始高斯态，纠缠呈扩散式增长（$S \sim t^{1/2}$）。在晚期$t \gtrsim \mathcal{O}(L^{2})$时，熵弛豫到我们精确计算出的面积律值。我们提出了一种修正的准粒子图像，它能解释所有这些主要特征，并且与我们基本精确的数值结果在定量上吻合良好。这些准粒子与非厄米有效哈密顿量的模式相关。在小波矢$k$下，准粒子以有限速度输运熵，但其寿命按$1/k^2$缩放；这两个条件的共同作用直接导致了观测到的$t^{1/2}$增长。

英文摘要：

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.

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