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We consider the single hole dynamics in a modified $t-J$ model at finitetemperature. The modified model includes a next nearest ($t'$) and next-nextnearest ($t''$) hopping. The model has been considered before in the zerotemperature limit to explain angle resolved photo-emission measurements. Weextend this consideration to the case of finite temperature where long-rangeanti-ferromagnetic order is destroyed, using the self-consistent Bornapproximation. The Dyson equation which relates the single hole Green'sfunctions for a fixed pseudo-spin and for fixed spin is derived. The Green'sfunction with fixed pseudo-spin is infrared stable but the Green's functionwith fixed spin is close to an infrared divergency. We demonstrate how torenormalize this Green's function in order to assure numerical convergence. Atnon-zero temperature the quasi-particle peaks are found to shift down in energyand to be broadened.Comment: 7 pages, RevTex, 5 Postscript figure

Single-hole Green’s functions in insulating copper oxides at nonzero temperature