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

TL;DR

This study uses the DMRG technique to identify and analyze the emergence of XXZ-like behavior in the phase diagram of an extended anisotropic Heisenberg chain, focusing on correlation functions and critical exponents.

Contribution

It provides detailed analysis of correlation functions and identifies a critical J' value where the decay exponent becomes independent of in-plane coupling, advancing understanding of phase behavior.

Findings

Agreement with exact XXZ model solutions

Identification of a critical J' value for phase transition

Detailed correlation function analysis

Abstract

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 ($J-J'$) 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 ($J'=0$) to benchmark our results, which clearly show the expected agreement. A critical value of $J'$ has been found where the relevant power-law decay exponent is independent of the in-plane nearest-neighbor coupling.