# Quantum fidelity approach to the ground state properties of the 1D ANNNI model in a transverse field

## TL;DR

This paper uses quantum fidelity to analyze the ground-state phases of the 1D ANNNI model in a transverse field, revealing multiple phases and phase transition types.

## Contribution

It introduces a numerical fidelity susceptibility approach to map the phase diagram of the 1D ANNNI model, predicting an infinite number of modulated phases.

## Key findings

- Identified ferromagnetic, paramagnetic, floating, and $raket{2,2}$ phases.
- Found second-order transition lines between modulated phases.
- Suggested a first-order transition between floating and $raket{2,2}$ phases.

## Abstract

In this work we analyze the ground-state properties of the $s=1/2$ one-dimensional ANNNI model in a transverse field using the quantum fidelity approach. We numerically determined the fidelity susceptibility as a function of the transverse field $B_x$ and the strength of the next-nearest-neighbor interaction $J_2$, for systems of up to 24 spins. We also examine the ground-state vector with respect to the spatial ordering of the spins. The ground-state phase diagram shows ferromagnetic, paramagnetic, floating, $\Braket{2,2}$ phases, and we predict an infinite number of modulated phases in the thermodynamic limit ($L \rightarrow \infty$). The transition lines separating the modulated phases seem to be of second-order, whereas the line between the floating and the $\Braket{2,2}$ phases is possibly of first-order.