Density-matrix based numerical methods for discovering order and correlations in interacting systems

TL;DR

This paper reviews advanced density-matrix based numerical methods for unbiased detection of order parameters and correlations in many-body interacting systems, extending existing techniques and demonstrating their application to complex quantum models.

Contribution

It introduces improvements to the quasi-degenerate density matrix method, extending it to arbitrary symmetry breaking cases, and surveys the correlation density matrix approach for analyzing correlations.

Findings

Extended QDDM method to arbitrary symmetry breaking

Applied methods to spinless bosons on a triangular lattice

Analyzed a spin-1/2 antiferromagnetic system at percolation threshold

Abstract

We review recently introduced numerical methods for the unbiased detection of the order parameter and/or dominant correlations, in many-body interacting systems, by using reduced density matrices. Most of the paper is devoted to the "quasi-degenerate density matrix" (QDDM) which is rooted in Anderson's observation that the degenerate symmetry-broken states valid in the thermodynamic limit, are manifested in finite systems as a set of low-energy "quasi-degenerate" states (in addition to the ground state). This method, its original form due to Furukawa et al.[Phys. Rev. Lett. 96, 047211 (2006)], is given a number of improvements here, above all the extension from two-fold symmetry breaking to arbitrary cases. This is applied to two test cases (1) interacting spinless hardcore bosons on the triangular lattice and (2) a spin-1/2 antiferromagnetic system at the percolation threshold. In addition, we survey a different method called the "correlation density matrix", which detects (possibly long-range) correlations only from the ground state, but using the reduced density matrix from a cluster consisting of two spatially separated regions.