Friedel oscillations induced by open boundary conditions in a two-band Hubbard model for CuO chains are numerically studied. We find that for physically realistic parameters and close to quarter filling, these oscillations have a ${2k}_F$ modulation according with experimental results on ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{7-\delta }.$ In addition, we predict that, for the same parameters, as hole doping is reduced from quarter filling to half filling, Friedel oscillations would acquire a ${4k}_F$ modulation, typical of a strongly correlated electron regime. The ${4k}_F$ modulation also dominates in the electron doped region. The range of parameters varied is very broad, and hence the results reported could apply to other cuprates and other strongly correlated compounds with quasi-one-dimensional structures. On a more theoretical side, we stress the fact that the copper and oxygen subsystems should be described by two different Luttinger liquid exponents.

• Received 30 August 2003

DOI:https://doi.org/10.1103/PhysRevB.69.014513