On reduced density matrices for disjoint subsystems

TL;DR

This paper investigates how different representations in quantum chains affect the reduced density matrices of disjoint subsystems, revealing that spin and fermion descriptions generally yield different results.

Contribution

It demonstrates that spin and fermion representations produce different reduced density matrices for disjoint subsystems in solvable quantum chains, highlighting the importance of representation choice.

Findings

Different reduced density matrices for spin and fermion representations in disjoint subsystems.

The effect observed in XX, XY, and transverse Ising chains.

Implications for quantum information and entanglement studies.

Abstract

We show that spin and fermion representations for solvable quantum chains lead in general to different reduced density matrices if the subsystem is not singly connected. We study the effect for two sites in XX and XY chains as well as for sublattices in XX and transverse Ising chains.