# Entanglement Hamiltonian of quantum critical chains and conformal field theories

## TL;DR

This paper investigates the effectiveness of the Bisognano-Wichmann ansatz in modeling entanglement Hamiltonians of quantum critical chains, demonstrating its accuracy in reproducing entanglement entropy scaling and corrections predicted by conformal field theory across various models.

## Contribution

It provides a comprehensive numerical validation of the BW-ansatz for quantum critical chains, showing its accuracy in capturing entanglement properties and potential for broader applications.

## Key findings

- BW Re9nyi entropies match CFT scaling predictions
- Norm distance between exact and BW density matrices decreases with system size
- BW-ansatz accurately predicts eigenvector properties and entanglement measures

## Abstract

We consider a lattice version of the Bisognano-Wichmann (BW) modular Hamiltonian as an ansatz for the bipartite entanglement Hamiltonian of the quantum critical chains. Using numerically unbiased methods, we check the accuracy of the BW-ansatz by both comparing the BW R\'enyi entropy to the exact results, and by investigating the size scaling of the norm distance between the exact reduced density matrix and the BW one. Our study encompasses a variety of models, scanning different universality classes, including transverse field Ising, Potts and XXZ chains. We show that the R\'enyi entropies obtained via the BW ansatz properly describe the scaling properties predicted by conformal field theory. Remarkably, the BW R\'enyi entropies faithfully capture also the corrections to the conformal field theory scaling associated to the energy density operator. In addition, we show that the norm distance between the discretized BW density matrix and the exact one asymptotically goes to zero with the system size: this indicates that the BW-ansatz can be also employed to predict properties of the eigenvectors of the reduced density matrices, and is thus potentially applicable to other entanglement-related quantities such as negativity.