Single and Many Particle Correlation Functions and Uniform Phase Bases for Strongly Correlated Systems

TL;DR

This paper introduces a new correlated basis for strongly correlated low-dimensional systems, demonstrating its effectiveness through analysis of a quasi-1D lattice model with distinct magnetic phases.

Contribution

A novel trial basis is proposed and applied to a quasi-1D lattice model, enabling better description of correlation functions and ground state properties.

Findings

Single particle correlations decay as a power law in the paramagnetic phase

The model exhibits both paramagnetic and Nagaoka ferromagnetic regions

The basis facilitates a mean-field BCS-type analysis with long-range order

Abstract

The need for suitable many or infinite fermion correlation functions to describe some low dimensional strongly correlated systems is discussed. This is linked to the need for a correlated basis, in which the ground state may be postive definite, and in which single particle correlations may suffice. A particular trial basis is proposed, and applied to a certain quasi-1D model. The model is a strip of the 2D square lattice wrapped around a cylinder, and is related to the ladder geometries, but with periodic instead of open boundary conditions along the edges. Analysis involves a novel mean-field approach and exact diagonalisation. The model has a paramagnetic region and a Nagaoka ferromagnetic region. The proposed basis is well suited to the model, and single particle correlations in it have power law decay for the paramagnet, where the charge motion is qualitatively hard core bosonic. The mean field also leads to a BCS-type model with single particle long range order.