Magnetic and Pairing Correlations in Correlated Electron Systems

TL;DR

This paper derives rigorous bounds on magnetic and pairing correlations in Hubbard and t-J models, providing insights into their temperature dependence and conditions for long-range order.

Contribution

It introduces new upper bounds for correlation functions in Hubbard and t-J models, clarifying their decay behavior and ruling out long-range order in certain cases.

Findings

Spin-spin correlation decay cannot be slower than inverse squared law at low temperatures.

On-site pairing correlation decay cannot be slower than inverse law.

Bounds suggest conditions where magnetic and pairing long-range order are impossible.

Abstract

Magnetic and superconducting pairing correlation functions in a general class of Hubbard models, the t-J model and a single-band Hubbard model with additional bond-charge interaction are investigated, respectively. Some rigorous upper bounds of the corresponding correlation functions are obtained. It is found that the decay of the spin-spin correlation function with temperature in the general Hubbard models can not be slower than the squared inverse law at low temperatures and the inverse law at high temperatures, while the on-site pairing correlation function can not be slower than the inverse law. An upper bound for the average energy of the t-J model is found. The upper bounds for the spin-spin and the electron pairing correlation functions in the t-J model as well as in the Hubbard model with bond-charge interaction are also obtained. These bounds are expected to provide certain standards for approximate methods. In some special cases, these bounds rule out the possibility of corresponding magnetic and pairing long-range order.