Holographic duality between $(2+1)$-d quantum anomalous Hall state and $(3+1)$-d topological insulators

TL;DR

This paper establishes a holographic duality between 2+1D quantum anomalous Hall states and 3+1D topological insulators, providing new insights into their topological properties via entanglement and response analysis.

Contribution

It introduces an exact holographic mapping that relates quantum anomalous Hall states to higher-dimensional topological insulators, offering a novel dual perspective.

Findings

Holographic dual of a quantum anomalous Hall state is a 3+1D topological insulator.

Topological response properties are consistent across the duality.

Entanglement spectrum reveals topological features in the dual description.

Abstract

In this paper, we study $(2+1)$-dimensional quantum anomalous Hall states, i.e. band insulators with quantized Hall conductance, using the exact holographic mapping. The exact holographic mapping is an approach to holographic duality which maps the quantum anomalous Hall state to a different state living in $(3+1)$-dimensional hyperbolic space. By studying topological response properties and the entanglement spectrum, we demonstrate that the holographic dual theory of a quantum anomalous Hall state is a $(3+1)$-dimensional topological insulator. The dual description enables a new characterization of topological properties of a system by the quantum entanglement between degrees of freedom at different length scales.