Area Law Micro-State Entropy from Criticality and Spherical Symmetry

TL;DR

This paper presents a non-gravitational model where micro-state entropy scales with the area of a sphere, demonstrating a form of holography through criticality and spherical symmetry in a bosonic field system.

Contribution

It introduces a non-relativistic bosonic model on a sphere that exhibits area-law entropy and holographic behavior at a quantum critical point, independent of gravity.

Findings

Entropy scales with the area of a (d-1)-sphere.

Presence of gapless modes at criticality matches the area.

Exact micro-state counting achieved via double-scaling limit.

Abstract

It is often assumed that the area law of micro-state entropy and the holography are intrinsic properties exclusively of the gravitational systems, such as black holes. We construct a non-gravitational model that exhibits an entropy that scales as area of a sphere of one dimension less. It is represented by a non-relativistic bosonic field living on a d-dimensional sphere of radius R and experiencing an angular-momentum-dependent attractive interaction. We show that the system possesses a quantum critical point with the emergent gapless modes. Their number is equal to the area of a (d-1)-dimensional sphere of the same radius R. These gapless modes create an exponentially large number of degenerate micro-states with the corresponding micro-state entropy given by the area of the same (d-1)-dimensional sphere. Thanks to a double-scaling limit, the counting of the entropy and of the number of the gapless modes is made exact. The phenomenon takes place for arbitrary number of dimensions and can be viewed as a version of holography.