Entanglement Scaling in the One-Dimensional Hubbard Model at Criticality

TL;DR

This paper derives exact formulas for local entanglement entropy in the 1D Hubbard model at criticality, linking its divergences to susceptibilities and revealing changes in local state accessibility during quantum phase transitions.

Contribution

It provides exact expressions for entanglement entropy at critical points and connects its divergence behavior to physical susceptibilities, offering new insights into quantum criticality.

Findings

Divergences of dE/dh and dE/du relate to spin and charge susceptibilities.

Logarithmic corrections indicate changes in local state accessibility.

Exact expressions for entanglement entropy at quantum critical points.

Abstract

We derive exact expressions for the local entanglement entropy E in the ground state of the one-dimensional Hubbard model at a quantum phase transition driven by a change in magnetic field h or chemical potential u. The leading divergences of dE/dh and dE/du are shown to be directly related to those of the zero-temperature spin and charge susceptibilities. Logarithmic corrections to scaling signal a change in the number of local states accessible to the system as it undergoes the transition.