Interferometric and Bipartite OTOC for Non-Markovian Open Quantum Spin-Chains and Lipkin-Meshkov-Glick Model

TL;DR

The paper investigates information scrambling in open quantum spin systems using interferometric $\,mathcal{F}$-OTOC and Haar-averaged bipartite OTOC, focusing on a spin-chain in a global LMG bath and a TFIM coupled to a local anisotropic bath, plus a closed LMG model to probe phase-driven chaos. It reveals that a global LMG environment generally suppresses light-cone–like spreading and accelerates scrambling via non-Markovian dynamics, while the tilted-field Ising model with a localized anisotropic bath exhibits clear ballistic light-cone propagation. The analysis shows that the LMG model exhibits chaos only in its symmetry-broken phase, with $\,mathcal{F}$-OTOC transitioning from periodic to irregular behavior across phases. Together, the findings demonstrate how bath topology and phase structure shape scrambling diagnostics, with $\,mathcal{F}$-OTOC and bipartite OTOC offering complementary insights into open-system quantum chaos and information dynamics.

Abstract

The information scrambling phenomena in an open quantum system modeled by Ising spin chains coupled to Lipkin-Meshkov-Glick (LMG) baths are observed via an interferometric method for obtaining out-of-time-ordered correlators ($\mathcal{F}-$OTOC). We also use an anisotropic bath connecting to a system of tilted field Ising spin chain in order to confirm that such situations are suitable for the emergence of ballistic spreading of information manifested in the light cones in the $\mathcal{F}-$OTOC profiles. Bipartite OTOC is also calculated for a bipartite open system, and its behavior is compared with that of the $\mathcal{F}-$OTOC of a two-spin open system to get a picture of what these measures reveal about the nature of scrambling in different parameter regimes. Additionally, the presence of distinct phases in the LMG model motivated an independent analysis of its scrambling properties, where $\mathcal{F}-$OTOC diagnostics revealed that quantum chaos emerges exclusively in the symmetry-broken phase.

Figures (8)

• Figure 1: The $\mathcal{F}(t)$ is plotted for the system of four spins under the LMG bath. Information scrambling is observed from the first spin, denoted by $\sigma_z^1$, to the other spins as depicted by the direction of the arrow. In (a), the $\mathcal{F}(t)$ is when $\lambda=0.5$ and (b) is when $\lambda=1$, where $\lambda$ is the constant of coupling to the bath. The other parameters are, $J_j=0.5$, $\omega_0=2$, $\omega_c=4, N = 5$, and $T=10$.
• Figure 2: The plot for $\mathcal{F}_c(t)$ when the system is of four spins under the LMG bath. Information scrambling is observed from the first spin, denoted by $\sigma_z^1$, to the other spins as depicted by the direction of the arrow. In (a), the $\mathcal{F}_c(t)$ is when $\lambda=0.5$, and (b) is when $\lambda=1$, where $\lambda$ is the constant of coupling to the bath. The other parameters are, $J_j=0.5$, $\omega_0=2$, $\omega_c=4, N = 5$, and $T=10$.
• Figure 3: $\mathcal{F}(t)$ in (a) and $G(\mathcal{E}^{\dagger})$ in (b) are plotted for two spins surrounded by an LMG bath. The bipartitions needed for calculating the bipartite OTOC, $G(\mathcal{E}^{\dagger})$, are taken as two two-qubit Hilbert spaces. The variations are shown for different coupling constants with the bath $\lambda$. The other parameters are, $J_j=0.5$, $\omega_0=2$, $\omega_c=4, N = 10$, and $T=10$.
• Figure 4: $\mathcal{F}(t)$ in (a) and $G(\mathcal{E}^{\dagger})$ in (b) are plotted for two spins surrounded by an LMG bath. The variations are shown for different bath frequencies $\omega_c$. The other parameters are, $J_j=0.5$, $\omega_0=2$, $\lambda=1$, $N = 10$, and $T=10$.
• Figure 5: $\mathcal{F}(t)$ in (a) and $G(\mathcal{E}^{\dagger})$ in (b) are plotted for two spins surrounded by an LMG bath. The variations are shown for different temperatures of the bath $T$. The other parameters are $J_j=0.5$, $\omega_0=2$, $\lambda=1$, $N = 10$, and $\omega_c=2$.