Entanglement generation and scaling from noisy quenches across a quantum critical point

TL;DR

This work analyzes how white noise in the transverse field affects entanglement generation when linearly quenching the transverse-field Ising chain across its quantum critical points. Using an exact noise-averaged master equation, it shows that noise drives a qualitative change in the scaling of two-spin entanglement, notably transforming the next-nearest-neighbor concurrence from a KZM-like $1/sqrt(tau)$ dependence to a logarithmic dependence on the quench time, and introduces a noise-dependent entanglement lifetime that scales as $(xi^2)^{-2/3}$. The study also reveals that, unlike defect densities, entanglement generation under noise is not simply linked to defect formation; however, the same 2/3 exponent emerges in the scaling of the entanglement-survival times with noise, hinting at a subtle connection. These results have implications for experiments on quantum simulators and annealers where noise is unavoidable, and they open questions about decoherence and entanglement in nonequilibrium critical dynamics.

Abstract

We study the impact of noise on the dynamics of entanglement in the transverse-field Ising chain, with the field quenched linearly across one or both of the quantum critical points of the model. Taking concurrence as a measure of entanglement, we find that a quench generates entanglement between nearest- and next-nearest-neighbor spins, with noise reducing the amount of entanglement. Focusing on the next-nearest-neighbor concurrence, known to exhibit Kibble-Zurek scaling with the square root of the quench rate in the noiseless case, we find a different result when noise is present: The concurrence now scales logarithmically with the quench rate, with a noise-dependent amplitude. This is also different from the ``anti-Kibble-Zurek" scaling of defect density with quench rate when noise is present, suggesting that noisy entanglement generation is largely independent from the rate of defect formation. Intriguingly, the critical time scale beyond which no entanglement is produced by a noisy quench scales as a power law with the strength of noise, with the same exponent as that which governs the optimal quench time for which defect formation is at a minimum in a standard quantum annealing scheme.

Figures (5)

• Figure 1: (Color online) Concurrence between two spins at time $t$ for a noiseless ramped quench of the transverse field in the TFI chain, from $h_i = -30$ at time $t=t_i$ to $h_f=h_0(t)$ for different values of time scale $\tau$: (a) nearest-neighbor spins, and (b) next-nearest-neighbor spins. System size: $N=200$.
• Figure 2: (Color online) Noise-averaged concurrence between two spins at time $t$ for a ramped quench of time scale $\tau=10$ with white noise of different intensities $\xi$ added to the transverse field of the TFI chain, with quench interval from $h_i=-30$ at $t=t_i$ to $h_f=h_0(t)$: (a) nearest-neighbor spins and (b) next-nearest-neighbor spins. System size: $N=200$.
• Figure 3: (Color online) Noise-averaged concurrence between two spins as a function of time scale $\tau$ for a ramped quench with added white noise of different intensities $\xi$, with quench interval from $h_i=-30$ to (a) $h_f = 5$ for nearest-neighbor spins, and (b) $h_f = 30$ for next-nearest-neighbor spins. System size: $N=200$.
• Figure 4: (Color online) (a) Power-law scaling $\tau_c(\xi) \sim \xi^{-\delta}$ with exponent $\delta = 0.666\pm0.001\approx2/3$, where $\xi$ is the noise intensity and $\tau_c(\xi)$ is the critical time scale at which the noise-averaged concurrence $\langle C_{\l,\l+2} \rangle$ vanishes. The inset shows the linear scaling of the maximum next-nearest-neighbor concurrence with $\xi^2$. (b) Noise-averaged concurrence between next-nearest-neighbor spins as functions of $\ln(\tau)$ for a ramped quench with added white noise for different values of noise intensity $\xi$, with quench interval from $h_i=-30$ to $h_f=30$.
• Figure 5: (Color online) The logarithm of the density of defects $n_{\xi}$ vs time scale $\tau$ of a ramped quench crossing a quantum critical point in the transverse field Ising chain for different noise intensities $\xi$. The behavior of the density of defects for different values of $\tau$ and $\xi$ illustrates anti-Kibble-Zurek behavior in the presence of a noisy ramp field.