Density Matrix Renormalization Group Study of the Disorder Line in the Quantum ANNNI Model

TL;DR

This study uses DMRG methods to precisely map the phase diagram of the quantum ANNNI model, identifying the transition and disorder lines, and analyzing critical behavior of the modulation parameter.

Contribution

The paper provides the first detailed numerical analysis of the disorder line in the quantum ANNNI model using DMRG and finite size scaling techniques.

Findings

Locates the ferromagnetic to paramagnetic transition line with high precision.

Supports the conjecture that the Peschel-Emery line coincides with the disorder line.

Finds the critical exponent for modulation vanishing as 1/2.

Abstract

We apply Density Matrix Renormalization Group methods to study the phase diagram of the quantum ANNNI model in the region of low frustration where the ferromagnetic coupling is larger than the next-nearest-neighbor antiferromagnetic one. By Finite Size Scaling on lattices with up to 80 sites we locate precisely the transition line from the ferromagnetic phase to a paramagnetic phase without spatial modulation. We then measure and analyze the spin-spin correlation function in order to determine the disorder transition line where a modulation appears. We give strong numerical support to the conjecture that the Peschel-Emery one-dimensional line actually coincides with the disorder line. We also show that the critical exponent governing the vanishing of the modulation parameter at the disorder transition is $\beta_q = 1/2$.