Zero-temperature magnetic ordering in the inhomogeneously frustrated quantum Heisenberg antiferromagnet on a square lattice

We examine the influence of homogeneous and inhomogeneous frustration on the ground-state ordering of the spin-1/2 ${\mathit{J}}_1$-${\mathit{J}}_2$ Heisenberg antiferromagnet on a square lattice with N=16 and N=20 sites. For a critical value of frustration ${\mathit{J}}_2^{\mathrm{crit}}$≊0.4${\mathit{J}}_1$ the conventional collinear antiferromagnetic long-range order is expected to break down in the homogeneously frustrated system. This critical frustration is drastically decreased by inhomogeneities simulating doping; we find ${\mathit{J}}_2^{\mathrm{crit}}$≊0.15${\mathit{J}}_1$, which is quite realistic for the situation in slightly doped cuprate superconductors. In the region of strong frustration a quantum spin-liquid state is realized without conventional collinear ordering. The properties of this quantum spin liquid are still under controversial discussion. Three different possibilities of a noncollinear ordering in the strongly frustrated region (${\mathit{J}}_2$≊0.5${\mathit{J}}_1$) are discussed: A dimerized (or spin-Peierls) state, a state with scalar chiral ordering, and a state with enhanced vector chiral correlations. In particular, owing to the possibility of excitations with fractional statistics and owing to experimental investigations of broken reflection symmetry and parity the symmetry properties of the chiral order parameters are of interest. The scalar chirality is odd under time reversal and two-dimensional reflection, whereas the vector chirality conserves the time-reversal symmetry. We find evidence for a vector chiral ordering as well as for a spin-Peierls state. These vector chiral correlations can be enhanced by local inhomogeneities (holes), whereas the spin-Peierls state is suppressed.