Single Hole Green's Functions in Insulating Copper Oxides at Nonzero Temperature

TL;DR

This paper investigates the behavior of single hole Green's functions in a modified $t-J$ model at finite temperature, revealing how quasi-particle peaks shift and broaden as temperature increases, using the self-consistent Born approximation.

Contribution

It extends previous zero-temperature studies to finite temperature, deriving Dyson equations and renormalization methods for Green's functions in a modified $t-J$ model.

Findings

Quasi-particle peaks shift downward with increasing temperature.

Green's functions with fixed pseudo-spin are infrared stable.

Green's functions with fixed spin require renormalization for convergence.

Abstract

We consider the single hole dynamics in a modified $t-J$ model at finite temperature. The modified model includes a next nearest ($t'$) and next-next nearest ($t''$) hopping. The model has been considered before in the zero temperature limit to explain angle resolved photo-emission measurements. We extend this consideration to the case of finite temperature where long-range anti-ferromagnetic order is destroyed, using the self-consistent Born approximation. The Dyson equation which relates the single hole Green's functions for a fixed pseudo-spin and for fixed spin is derived. The Green's function with fixed pseudo-spin is infrared stable but the Green's function with fixed spin is close to an infrared divergency. We demonstrate how to renormalize this Green's function in order to assure numerical convergence. At non-zero temperature the quasi-particle peaks are found to shift down in energy and to be broadened.