Random Walk of Bipartite Spins in a Classicalized Holographic Tensor Network

TL;DR

This paper models the AdS$_2$ space metric as a steady-state distribution of bipartite spins undergoing a random walk in a holographic tensor network, linking microscopic spin dynamics to emergent geometric structure.

Contribution

It introduces a microscopic statistical model of the AdS$_2$ metric using bipartite spins in a holographic tensor network, connecting spin distributions to emergent geometry.

Findings

The steady state of the random walk reproduces the AdS$_2$ metric.

Bipartite spin distribution induces a metric in the tensor network.

The model links microscopic spin configurations to macroscopic geometric space.

Abstract

We consider the random walk of spin-zero bipartite spins in the classicalized holographic tensor network of the ground state of a strongly coupled two-dimensional conformal field theory. The bipartite-spin distribution induces a metric in this network. In the steady state of the random walk, the induced metric gives the two-dimensional anti-de Sitter (AdS$_2$) space metric. We consider this distribution as a microscopic statistical model of the AdS$_2$ space metric.