Theoretical study of Cu-O chain fragments in the oxygen-deficient planes of ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{6+\mathit{x}}$. I. Microscopic properties

We examine some models of the strongly correlated ⋅⋅⋅Cu-O⋅⋅⋅ chain fragments that are the main components of the oxygen-deficient planes of ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{6+\mathit{x}}$. We use quantum Monte Carlo methods, exact numerical diagonalization as well as an analytical approach in order to study the thermodynamic properties of the chain fragments and the charge and magnetic correlations within them as functions of the concentration of carriers and of the temperature. Only the fermionic degrees of freedom of the chain fragments are considered. © 1996 The American Physical Society.