Floating Phase in 1D Transverse ANNNI Model

TL;DR

This paper investigates the ground state phases of the 1D transverse ANNNI model using perturbative methods, revealing the existence of a floating phase between ferromagnetic and antiphase regions.

Contribution

It introduces two perturbative approaches to analyze the phase diagram of the transverse ANNNI model, identifying phase transition lines and confirming the floating phase presence.

Findings

Only two phase transition lines from the critical point

Floating phase exists for small transverse fields

Perturbation methods effectively analyze complex quantum phases

Abstract

To study the ground state of ANNNI chain under transverse field as a function of frustration parameter $\kappa$ and field strength $\Gamma$, we present here two different perturbative analyses. In one, we consider the (known) ground state at $\kappa=0.5$ and $\Gamma=0$ as the unperturbed state and treat an increase of the field from 0 to $\Gamma$ coupled with an increase of $\kappa$ from 0.5 to $0.5+r\Gamma$ as perturbation. The first order perturbation correction to eigenvalue can be calculated exactly and we could conclude that there are only two phase transition lines emanating from the point $\kappa=0.5$, $\Gamma=0$. In the second perturbation scheme, we consider the number of domains of length 1 as the perturbation and obtain the zero-th order eigenfunction for the perturbed ground state. From the longitudinal spin-spin correlation, we conclude that floating phase exists for small values of transverse field over the entire region intermediate between the ferromagnetic phase and antiphase.