Entanglement of heterogeneous free fermion chains

TL;DR

This paper investigates the entanglement entropy in heterogeneous free fermion chains, revealing different scaling behaviors depending on the criticality of the parts, including logarithmic and area law regimes with unique convergence properties.

Contribution

It provides a detailed analysis of entanglement entropy in mixed fermionic chains, highlighting new scaling behaviors at Lifshitz points and critical interfaces.

Findings

Logarithmic entanglement scaling in conformally critical parts.

Area law behavior with convergence variations in non-critical cases.

Algebraic convergence with fractional indices at Lifshitz points.

Abstract

We calculate the ground state entanglement entropy between two heterogeneous parts of a free fermion chain. The two parts could be XX chains with different parameters or an XX half chain connected with a quantum Ising half chain. It is shown that logarithmic behavior holds if the two parts are conformally critical. In other cases, area law holds with abundant convergence behaviors. In particular, when XX chain at Lifshitz point is connected with a conformally or Lifshitz critical part, entanglement entropy converges algebraically with a fractional subleading index.