Correlation density matrices for 1- dimensional quantum chains based on the density matrix renormalization group

TL;DR

This paper introduces the use of correlation density matrices derived from density matrix renormalization group methods to analyze long-range correlations in one-dimensional quantum chains, providing both theoretical and numerical insights.

Contribution

It presents a method to extract and analyze correlations in quantum chains using correlation density matrices obtained via matrix product states, with detailed practical guidance.

Findings

Correlation density matrices reveal detailed correlation structures.

The method efficiently identifies operators responsible for long-range correlations.

Numerical results demonstrate the approach's effectiveness in spinless extended Hubbard models.

Abstract

A useful concept for finding numerically the dominant correlations of a given ground state in an interacting quantum lattice system in an unbiased way is the correlation density matrix. For two disjoint, separated clusters, it is defined to be the density matrix of their union minus the direct product of their individual density matrices and contains all correlations between the two clusters. We show how to extract from the correlation density matrix a general overview of the correlations as well as detailed information on the operators carrying long-range correlations and the spatial dependence of their correlation functions. To determine the correlation density matrix, we calculate the ground state for a class of spinless extended Hubbard models using the density matrix renormalization group. This numerical method is based on matrix product states for which the correlation density matrix can be obtained straightforwardly. In an appendix, we give a detailed tutorial introduction to our variational matrix product state approach for ground state calculations for 1- dimensional quantum chain models. We show in detail how matrix product states overcome the problem of large Hilbert space dimensions in these models and describe all techniques which are needed for handling them in practice.