Holographic Local Quenches and Entanglement Density (1302.5703v2)

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.

• The paper establishes a holographic model where free-falling particles in AdS space emulate local quenches, demonstrating logarithmic growth in entanglement entropy.
• It introduces entanglement density as a novel metric that measures localized quantum entanglement with conserved spatial distribution.
• The study reveals a direct link between the energy of massive objects in holographic setups and the corresponding quantum informational content.

Overview of Holographic Local Quenches and Entanglement Density

The paper by Masahiro Nozaki, Tokiro Numasawa, and Tadashi Takayanagi presents a detailed investigation of local quenches in quantum field theories utilizing holography, specifically within the framework of the AdS/CFT correspondence. The authors explore how local quenches—characterized by localized disturbances in a quantum system—can be modeled holographically by free-falling particles in Anti-de Sitter (AdS) space. The paper focuses on calculating the time evolution of the holographic entanglement entropy (HEE), revealing insights into quantum entanglement dynamics following local perturbations.

In essence, the paper provides a methodological approach to studying local quenches via holography, extending previous analyses primarily focused on global quenches. The research introduces the concept of entanglement density, which aids in evaluating the quantum entanglement structure within quenched systems.

Key Findings

1. Holographic Model of Local Quenches:
   • The authors establish a model where a massive particle falls freely in AdS spacetime to represent a local quench. This model facilitates the examination of the holographic entanglement entropy during the quench process and confirms the presence of a logarithmic growth pattern typical in such systems.
2. Entanglement Density:
   • A salient contribution of this research is the concept of entanglement density. This quantity measures the density of entangled pairs between two positions within a system and offers a finer granularity of entanglement structures than merely computing entanglement entropy.
3. Energy-Information Relationship:
   • The paper postulates a direct correlation between the quantum information embodied by a massive object in a holographic setup and its total energy, inferred from the framework of AdS/CFT duality.
4. Exact Analysis for Lower Dimensions:
   • For two-dimensional systems, the authors execute explicit computations under local quenches, obtaining exact expressions for entanglement entropy which align with general expectations in conformal field theories.
5. Conservation and Positive Nature of Entanglement Density:
   • Leveraging strong subadditivity, the paper proves the positivity of entanglement density, confirming its validity as a physical measure. Furthermore, the total integration of entanglement density is conserved over time, echoing the conservation laws at play in fundamental quantum mechanical systems.

Implications and Future Directions

The paper's findings have far-reaching implications for both theoretical physics and the development of quantum technologies. Practically, understanding how entanglement evolves in response to local perturbations can potentially inform techniques for managing quantum information in various physical systems, including cold atoms and quantum computing.

The introduction of entanglement density opens avenues for novel analytic tools in the examination of quantum systems, promoting a deeper understanding of the spatial distribution of entanglement and its dynamics.

Future work can expand upon these results by considering more complex systems, such as higher-dimensional setups, or by introducing additional factors like quantum fields of different types. Moreover, exploring the universality of the suggested energy-information relationship across different quantum field theories and gravitational duals could enhance our comprehension of holographic principles.

Overall, the paper advances the field by providing fresh insights into the time evolution of quantum entanglement and introducing new conceptual tools like entanglement density, paving the way for future explorations into the holographic modeling of quantum dynamical processes.