Incommensurate correlations in thet-Jand frustrated spin-1/2 Heisenberg models

We analyze the possible existence of incommensurate correlations in the t-J model as a function of doping and in the ${\mathit{J}}_1$-${\mathit{J}}_2$-${\mathit{J}}_3$ spin-1/2 Heisenberg model as a function of frustration using exact diagonalization techniques on small lattices. For the t-J model we found that when holes are introduced the spin structure factor S(q) shifts the position of its maximum away from (π,π). However, we do not observe indications of the existence of long-range incommensurate order. The frustrated Heisenberg model is analyzed using spin-wave techniques. We present the phase diagram including 1/S corrections. It has special regions where there is no magnetic order that are natural candidates for new nonclassical ground states. Using a Lanczos method we study the line ${\mathit{J}}_3$=${\mathit{J}}_2$/2, which is completely disordered in the spin-wave analysis for ${\mathit{J}}_2$/${\mathit{J}}_1$>1/4. S(q) behaves as in the t-J model replacing doping by frustration. We also study the square of order parameters related with Néel, twisted, dimer, and chiral order. After the Néel order is destabilized by frustration, the twisted and dimer states are enhanced. On the other hand, there are no indications that the uniform or staggered chiral state can be the ground state of the frustrated Heisenberg model.