On the reduced density matrix for a chain of free electrons

TL;DR

This paper investigates the properties of the reduced density matrix in an infinite chain of free electrons, deriving analytical eigenfunctions and exploring connections to the six-vertex model.

Contribution

It introduces a commuting operator for the reduced density matrix in free electron chains and analytically determines eigenfunctions at half filling in the continuum limit.

Findings

Identified a commuting operator for the reduced density matrix.

Derived analytical eigenfunctions for dominant eigenvalues.

Discussed relations to the critical six-vertex model.

Abstract

The properties of the reduced density matrix describing an interval of N sites in an infinite chain of free electrons are investigated. A commuting operator is found for arbitrary filling and also for open chains. For a half filled periodic chain it is used to determine the eigenfunctions for the dominant eigenvalues analytically in the continuum limit. Relations to the critical six-vertex model are discussed.