The phase diagram of the extended anisotropic ferromagnetic-antiferromagnetic Heisenberg chain

TL;DR

This study uses DMRG to map the phase diagram of a 1D extended anisotropic Heisenberg model with competing ferromagnetic and antiferromagnetic interactions, identifying multiple phases and their correlation properties.

Contribution

It provides the first detailed phase diagram of the extended anisotropic Heisenberg chain with boundary analysis and finite-size scaling, classifying various quantum phases.

Findings

Identified two gapless spin-fluid phases.

Detected two phases with massive excitations.

Mapped phase boundaries using finite-size scaling.

Abstract

By using Density Matrix Renormalization Group (DMRG) technique we study the phase diagram of 1D extended anisotropic Heisenberg model with ferromagnetic nearest-neighbor and antiferromagnetic next-nearest-neighbor interactions. We analyze the static correlation functions for the spin operators both in- and out-of-plane and classify the zero-temperature phases by the range of their correlations. On clusters of $64,100,200,300$ sites with open boundary conditions we isolate the boundary effects and make finite-size scaling of our results. Apart from the ferromagnetic phase, we identify two gapless spin-fluid phases and two ones with massive excitations. Based on our phase diagram and on estimates for the coupling constants known from literature, we classify the ground states of several edge-sharing materials.