A Microscopic Model of Holography: Survival by the Burden of Memory

TL;DR

This paper presents a microscopic quantum model demonstrating holographic states with area-law entropy, showing that states with heavier memory loads are more stable, and suggesting universality in systems with high memory capacity.

Contribution

It introduces a simple quantum model realizing holography with area-law entropy and reveals that memory load influences state stability, offering insights into black hole information retention.

Findings

Holographic states exhibit area-law entropy.

States with heavier memory loads survive longer.

Pattern off-loading leads to entanglement and scrambling.

Abstract

An explicit microscopic realization of the phenomenon of holography is provided by a class of simple quantum theories of a bosonic field inhabiting a d-dimensional space and experiencing a momentum dependent attractive interaction. An exact mode counting reveals a family of holographic states. In each a set of gapless modes emerges with their number equal to the area of a (d-1)-dimensional sphere. These modes store an exponentially large number of patterns within a microscopic energy gap. The resulting micro-state entropy obeys the area-law reminiscent of a black hole entropy. We study the time-evolution of the stored patterns and observe the following phenomenon: Among the degenerate micro-states the ones with heavier loaded memories survive longer than those that store emptier patterns. Thus, a state gets stabilized by the burden of its own memory. From time to time the information pattern gets off-loaded from one holographic state into another but cannot escape the system. During this process the pattern becomes highly entangled and scrambled. We suggest that this phenomenon is universal in systems with enhanced memory storage capacity, such as black holes or critical neural networks. This universality sheds an interesting light on the puzzle of why, despite the evaporation, is a black hole forced to maintain information internally for a very long time.