Single-site entanglement at superconductor-insulator transition in the Hirsch model

TL;DR

This paper studies the superconductor-insulator transition in a one-dimensional Hubbard model with bond-charge interaction, using entanglement and finite size scaling to identify the quantum phase transition point.

Contribution

It introduces a combined approach of entanglement derivatives and finite size scaling to precisely locate the transition in the Hirsch model.

Findings

Quantum phase transition occurs at finite Coulomb interaction u_c(x) for x>0.5.

The insulating state emerges beyond the critical interaction u_c.

The region below u_c exhibits superconducting characteristics for certain x values.

Abstract

We investigate the transition to the insulating state in the one-dimensional Hubbard model with bond-charge interaction x (Hirsch model), at half-filling and T=0. By means of the density-matrix renormalization group algorithm the charge gap closure is examined by both standard finite size scaling analysis and looking at singularities in the derivatives of single-site entanglement. The results of the two techniques show that a quantum phase transition takes place at a finite Coulomb interaction u_c(x) for x>0.5. The region 0<u<u_c turns out to have a superconducting nature, at least for not too large x>x_c.