Holographic local quenches and entanglement density

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.

Entanglement negativity after a local quantum quench in conformal field theories

“…In particular, for different methods of local quenches [21,22,[28][29][30], the shape of entangled pairs may be very different. A quantitative study of this question as well as its application to the finite temperature case will be reported elsewhere [40].…”

“…Second, by neglecting various nonuniversal terms, we arrive at the same result as in Eq. (28). The difference is that for asymmetric intervals, we have different expressions of w ij , as explicitly given in the appendix.…”

“…In our work, a local quantum quench is realized by joining two separate CFTs at the endpoints. Another method to realize a local quantum quench is through acting with a local operator on an infinitely extended system [28][29][30]. By studying the increase of the Renyi entropy at a later time, quantum entanglement of local operators can be detected.…”

“…pairs [28][29][30][31][32] which carry entanglement information. When the entangled pairs arrive at two intervals separately, the entanglement negativity can be built immediately.…”

Holographic geometry of cMERA for quantum quenches and finite temperature

“…It will also be interesting to find a cMERA description of localized excitations instead of the translationally invariant ones discussed in this paper. This will be related to the local quenches [42] and there have been examples of their gravity duals [43][44][45][46]. One more intriguing future problem is to explore universal properties of excited states from the viewpoint of cMERA (refer to recent results from holography and CFT calculations [47][48][49][50][51][52][53][54]).…”