Holographic Local Quenches and Entanglement Density

TL;DR

The paper presents a holographic model for local quantum quenches using a freely falling massive particle in AdS, deriving the backreacted geometry and holographic stress tensor to capture localized excitations. It develops a perturbative and exact treatment of holographic entanglement entropy under local quenches, introduces the entanglement density to analyze spatial entanglement structure, and reveals a linear-energy–size relation for the maximal information carried by a localized object. The work connects entanglement dynamics to thermodynamics and gravity, offering a MERA-based interpretation of the emergent geometry and proposing that gravitational force reflects entanglement redistribution. These results advance the understanding of non-equilibrium entanglement propagation in higher-dimensional CFTs and provide quantitative tools for characterizing local quenches holographically.

Abstract

We propose a free falling particle in an AdS space as a holographic model of local quench. Local quenches are triggered by local excitations in a given quantum system. We calculate the time-evolution of holographic entanglement entropy. We confirm a logarithmic time-evolution, which is known to be typical in two dimensional local quenches. To study the structure of quantum entanglement in general quantum systems, we introduce a new quantity which we call entanglement density and apply this analysis to quantum quenches. We show that this quantity is directly related to the energy density in a small size limit. Moreover, we find a simple relationship between the amount of quantum information possessed by a massive object and its total energy based on the AdS/CFT.

Figures (19)

• Figure 1: Setups of local quenches. The upper picture describes a process of jointing two systems which are defined on semi-infinite lines. The lower one describes localized excitations on an infinitely extended system. We define the parameter $\alpha$ which measures the size of excited region at the beginning of the local quench.
• Figure 2: A falling massive particle in AdS and the calculation of holographic entanglement entropy for two different choices of the subsystem $A$. It is clear from this picture that the back reaction due to the falling particle gets significant when $l=z(t)$ in the left picture and $t=0$ in the right one because the particle is on top of $\gamma_A$.
• Figure 3: The profiles of the energy density $T_{tt}$ for $d=2$ (left), $d=3$ (middle) and $d=4$ (right) as a function of $\rho$ and $t$ within the range $-5<t<5$. We set $\alpha=R=M=G_N=1$.
• Figure 4: A sketch of time evolution of energy density and entangled pairs for $d=2$. The understanding of detailed structure of quantum entanglement and entangled pairs is the main subject of this paper as will be studied in later sections.
• Figure 5: The plots of $\Delta S_A$ at $\xi=0$ for $d=3$. The left and middle one describe $S_A$ as a function of $t$. We choose $(\alpha,l)=(1,5)$ (left) and $(\alpha,l)=(1,0.5)$ (middle), respectively. The right 3d graph expresses $S_A$ as a function of $t$ and $l$ for $\alpha=1$. The horizontal coordinate corresponds to $l$. We took the range $-10<t<10$ and $0<l<10$. We set $R=4G_N=M=1$.