Exact holographic mapping in free fermion systems

TL;DR

This paper provides an analytical study of the Exact Holographic Mapping in free fermion systems, confirming previous numerical results and exploring new bulk geometries, thereby deepening understanding of holographic duality in quantum many-body systems.

Contribution

It offers the first analytical results for free-fermion systems within the Exact Holographic Mapping, clarifying bulk-boundary relationships and exploring new geometries beyond prior numerical work.

Findings

Confirmed numerical results with analytic solutions

Analyzed near horizon black hole regimes

Explored bulk geometries for boundary critical fermions

Abstract

In this paper, we shall perform a detailed analysis of the Exact Holographic Mapping first introduced in arXiv:1309.6282, which was proposed as an explicit example of holographic duality between quantum many-body systems and gravitational theories. We obtain analytic results for free-fermion systems that not only confirm previous numerical results, but also elucidate the exact relationships between the various physical properties of the bulk and boundary systems. Our analytic results allow us to study the asymptotic properties that are difficult to probe numerically, such as the near horizon regime of the black hole geometry. We shall also explore a few interesting but hitherto unexplored bulk geometries, such as that corresponding to a boundary critical fermion with nontrivial dynamic critical exponent. Our analytic framework also allows us to study the holographic mapping of some of these boundary theories in dimensions 2+1 or higher.