Density Matrices for a Chain of Oscillators

TL;DR

This paper investigates the structure of reduced density matrices in chains of oscillators with optical phonon spectra, revealing they are exponentials of bosonic operators and analyzing their spectra through a connection to 2D Gaussian models.

Contribution

It demonstrates that reduced density matrices in such chains are exponentials of bosonic operators and characterizes their spectra, linking to a 2D Gaussian model for large systems.

Findings

Reduced density matrices are exponentials of bosonic operators.

Spectra of these matrices are exponential and explicitly determined.

Large system behavior relates to a two-dimensional Gaussian model.

Abstract

We consider chains with an optical phonon spectrum and study the reduced density matrices which occur in density-matrix renormalization group (DMRG) calculations. Both for one site and for half of the chain, these are found to be exponentials of bosonic operators. Their spectra, which are correspondingly exponential, are determined and discussed. The results for large systems are obtained from the relation to a two-dimensional Gaussian model.