Inversion phenomenon and phase diagram of the $S=1/2$ distorted diamond chain with the $XXZ$ interaction anisotropy

TL;DR

This paper investigates the phase diagram of an $S=1/2$ distorted diamond chain with $XXZ$ anisotropy, revealing an inversion phenomenon where the typical association of phases with anisotropy types is reversed due to frustration and trimer effects.

Contribution

It introduces the concept of an inversion phenomenon in the phase diagram of the $S=1/2$ distorted diamond chain with $XXZ$ anisotropy, combining perturbation theory and numerical analysis.

Findings

Inversion of anisotropy and wave-function properties in certain phase regions.

Identification of N{é}el and spin-fluid phases associated with XY-like and Ising-like anisotropies.

Elucidation of the roles of frustration, trimer structure, and $XXZ$ anisotropy in phase behavior.

Abstract

We discuss the anisotropies of the Hamiltonian and the wave-function in an $S=1/2$ distorted diamond chain. The ground-state phase diagram of this model is investigated using the degenerate perturbation theory up to the first order and the level spectroscopy analysis of the numerical diagonalization data. In some regions of the obtained phase diagram, the anisotropy of the Hamiltonian and that of the wave-function are inverted, which we call inversion phenomenon; the N\'{e}el phase appears for the XY-like anisotropy and the spin-fluid phase appears for the Ising-like anisotropy. Three key words are important for this nature, which are frustration, the trimer nature, and the $XXZ$ anisotropy.