Entanglement Entropy, Local IR/UV Connection and MPS in Weyl-deformed Geometries

TL;DR

This paper investigates how entanglement entropy in 2D CFTs responds to Weyl transformations, linking holographic IR/UV connections with matrix product state simulations in deformed geometries.

Contribution

It demonstrates the local IR cutoff deformation in AdS$_3$ due to Weyl transformations and explores entanglement entropy behavior using MPS in free fermion CFTs with inhomogeneous couplings.

Findings

Weyl deformations correspond to local IR cutoff changes in AdS$_3$

Numerical MPS results show entanglement entropy variations under background deformations

Challenges identified in applying DMRG to inhomogeneous interactions

Abstract

We study the behaviour of entanglement entropy in two-dimensional CFTs under Weyl transformations from the Weyl anomaly. Using the Ryu-Takayanagi-formula, we show that these deformations correspond to local deformations of the IR cutoff of AdS$_3$, which gives an example of the local validity of the IR/UV Connection in AdS/CFT. We then use Matrix Product States to demonstrate the behaviour of entanglement entropy under Weyl transformations in the two-dimensional free fermion CFT mapped to the XY-model with site-dependent coupling. We present numerical results for different deformations of the background and discuss issues arising for the standard DMRG procedure for the resulting inhomogeneous interactions due to a nontrivial background.