Reduced density matrices and entanglement entropy in free lattice models

TL;DR

This paper reviews the properties of reduced density matrices in free lattice models, focusing on their thermal form, spectra, and entanglement entropy across various dimensions and quench scenarios.

Contribution

It provides a comprehensive analysis of the structure and spectra of reduced density matrices in free lattice models, including their behavior after quenches.

Findings

Reduced density matrices have a thermal form in free models.

Spectral properties depend on system dimension and quench type.

Entanglement entropy can be computed from single-particle spectra.

Abstract

We review the properties of reduced density matrices for free fermionic or bosonic many-particle systems in their ground state. Their basic feature is that they have a thermal form and thus lead to a quasi-thermodynamic problem with a certain free-particle Hamiltonian. We discuss the derivation of this result, the character of the Hamiltonian and its eigenstates, the single-particle spectra and the full spectra, the resulting entanglement and in particular the entanglement entropy. This is done for various one- and two-dimensional situations, including also the evolution after global or local quenches.