Nematic Tomonaga-Luttinger Liquid Phase in an $S=1/2$ Ferromagnetic-Antiferromagnetic Bond-Alternating Chain

TL;DR

This study numerically maps the phase diagram of an $S=1/2$ bond-alternating chain with mixed ferromagnetic and antiferromagnetic interactions, revealing a wide nematic Tomonaga-Luttinger liquid phase and confirming it with perturbation theory.

Contribution

It provides the first detailed numerical phase diagram of the $S=1/2$ bond-alternating chain showing the emergence of the nematic TLL phase and validates it with perturbation calculations.

Findings

The phase diagram includes ferromagnetic, XY1, singlet-dimer, up-up-down-down, and nematic TLL phases.

The nematic TLL phase appears over a wide parameter region.

Perturbation theory from the strong ferromagnetic limit agrees with numerical phase boundaries.

Abstract

We numerically investigate the ground-state phase diagram of the $S=1/2$ ferromagnetic-antiferromagnetic bond-alternating chain, in which the ferromagnetic interactions are stronger than the antiferromagnetic ones, and the anisotropies of the former and latter interactions are of the Ising-type and the $XY$-type, respectively. We use various numerical methods, such as the level spectroscopy and phenomenological renormalization-group analyses of the numerical data obtained by the exact diagonalization method, and so on. The resultant phase diagrams contain the ferromagnetic, $XY$1, singlet-dimer, and up-up-down-down phases as well as the nematic Tomonaga-Luttinger liquid (nTLL) phase which appears in a wide region of the interaction parameters. Perturbation calculations from the strong limit of the ferromagnetic interactions reproduce fairly well the numerical results of the phase boundary lines associated with the nTLL phase in the phase diagrams.