Correlation density matrix: an unbiased analysis of exact diagonalizations

TL;DR

The paper introduces the correlation density matrix (CDM), a new unbiased method for analyzing correlations in quantum lattice models by decomposing the joint density matrix of separated clusters.

Contribution

It presents the CDM as a systematic, unbiased tool to identify dominant and unexpected correlations in ground state wavefunctions of interacting lattice models.

Findings

CDM effectively isolates correlation operators.

Singular value decomposition reveals dominant correlations.

Method uncovers unexpected correlation patterns.

Abstract

Given the ground state wavefunction for an interacting lattice model, we define a "correlation density matrix"(CDM) for two disjoint, separated clusters $A$ and $B$, to be the density matrix of their union, minus the direct product of their respective density matrices. The CDM can be decomposed systematically by a numerical singular value decomposition, to provide a systematic and unbiased way to identify the operator(s) dominating the correlations, even unexpected ones.