Fano resonances and entanglement entropy

TL;DR

This paper investigates how Fano resonances influence entanglement entropy in a fermionic chain with an impurity, revealing a continuous variation in the entropy scaling and providing explicit formulas validated by numerical data.

Contribution

It introduces a new explicit formula for entanglement entropy in impurity systems, highlighting the impurity's continuous impact on entropy scaling and its agreement with numerical results.

Findings

Logarithmic entanglement entropy scaling near the impurity

Explicit impurity contribution formula for entropy

Oscillating subleading term with open boundary conditions

Abstract

We study the entanglement in the ground state of a chain of free spinless fermions with a single side-coupled impurity. We find a logarithmic scaling for the entanglement entropy of a segment neighboring the impurity. The prefactor of the logarithm varies continuously and contains an impurity contribution described by a one-parameter function, while the contribution of the unmodified boundary enters additively. The coefficient is found explicitly by pointing out similarities with other models involving interface defects. The proposed formula gives excellent agreement with our numerical data. If the segment has an open boundary, one finds a rapidly oscillating subleading term in the entropy that persists in the limit of large block sizes. The particle number fluctuation inside the subsystem is also reported. It is analogous with the expression for the entropy scaling, however with a simpler functional form for the coefficient.