# Critical Entanglement for the Half-Filled Extended Hubbard Model

## TL;DR

This paper investigates phase transitions in the one-dimensional extended Hubbard model at half-filling by analyzing entanglement entropy with advanced DMRG techniques to accurately identify critical points.

## Contribution

It introduces a novel curve fitting and scaling method for precise detection of second-order and BKT critical points in the model.

## Key findings

- Accurate identification of critical points using entanglement entropy.
- Observation of finite-size and boundary effects.
- Method achieves accuracy comparable to previous studies.

## Abstract

We study the ground state of the one-dimensional extended Hubbard model at half-filling using the entanglement entropy calculated by Density Matrix Renormalization Group (DMRG) techniques. We apply a novel curve fitting and scaling method to accurately identify a $2^{nd}$ order critical point as well as a Berezinskii-Kosterlitz-Thouless (BKT) critical point. Using open boundary conditions and medium-sized lattices with very small truncation errors, we are able to achieve similar accuracy to previous authors. We also report observations of finite-size and boundary effects that can be remedied with careful pinning.