XXZ-like phase in the F-AF anisotropic Heisenberg chain

By means of the Density Matrix Renormalization Group technique, we have studied the region where $XXZ$-like behavior is most likely to emerge within the phase diagram of the F-AF anisotropic extended ($J-J^{\mathrm{\prime }}$) Heisenberg chain. We have analyzed, in great detail, the equal-time two-spin correlation functions, both in- and out-of- plane, as functions of the distance (and momentum). Then, we have extracted, through an accurate fitting procedure, the exponents of the asymptotic power-law decay of the spatial correlations. We have used the exact solution of $XXZ$ model ($J^{\mathrm{\prime }}=0$) to benchmark our results, which clearly show the expected agreement. A critical value of $J^{\mathrm{\prime }}$ has been found where the relevant power-law decay exponent is independent of the in-plane nearest-neighbor coupling.