# Flow Equation Holography

## TL;DR

This paper generalizes the holographic entanglement entropy concept from AdS/CFT to generic quantum many-body systems using a perturbative approach, deriving a relation between disentangling flow and min-entropy with illustrative examples.

## Contribution

It introduces a perturbative framework connecting a unitary disentangling flow to min-entropy in quantum systems, extending holographic ideas beyond AdS/CFT.

## Key findings

- Derived a simple expression linking disentangling flow to min-entropy.
- Explicit calculations for critical free fermions in 1D and 2D.
- Demonstrated the generalization of holographic entanglement concepts.

## Abstract

The Ryu-Takayanagi conjecture establishes a remarkable connection between quantum systems and geometry. Specifically, it relates the entanglement entropy to minimal surfaces within the setting of AdS/CFT correspondence. This Letter shows how this idea can be generalised to generic quantum many-body systems within a perturbative expansion where the region whose entanglement properties one is interested in is weakly coupled to the rest of the system. A simple expression is derived that relates a unitary disentangling flow in an emergent RG-like direction to the min-entropy of the region under consideration. Explicit calculations for critical free fermions in one and two dimensions illustrate this relation.