# Diversity of quantum ground states and quantum phase transitions of a spin-1/2 Heisenberg octahedral chain

## TL;DR

This paper explores the diverse quantum ground states and phase transitions in a spin-1/2 Heisenberg octahedral chain, revealing complex phases, magnetization plateaus, and thermodynamic behaviors through advanced analytical and numerical methods.

## Contribution

It provides a comprehensive analysis of the ground-state phase diagram and quantum phase transitions in a flat-band spin chain, including rigorous proofs and numerical results.

## Key findings

- Multiple quantum phases including ferrimagnetic, spin-liquid, and localized-magnon states.
- Observation of up to four magnetization plateaus at fractional values.
- Low-temperature peaks in specific heat near phase transitions.

## Abstract

The spin-1/2 Heisenberg octahedral chain with regularly alternating monomeric and square-plaquette sites is investigated using various analytical and numerical methods: variational technique, localized-magnon approach, exact diagonalization (ED) and density-matrix renormalization group (DMRG) method. The model belongs to the class of flat-band systems and it has a rich ground-state phase diagram including phases with spontaneously broken translational symmetry. Moreover, it exhibits an anomalous low-temperature thermodynamics close to continuous or discontinuous field-driven quantum phase transitions between three quantum ferrimagnetic phases, tetramer-hexamer phase, monomer-tetramer phase, localized-magnon phase and two different spin-liquid phases. If the intra-plaquette coupling is at least twice as strong as the monomer-plaquette coupling, the variational method furnishes a rigorous proof of the monomer-tetramer ground state in a low-field region and the localized-magnon approach provides an exact evidence of a single magnon trapped at each square plaquette in a high-field region. In the rest of parameter space we have numerically studied the ground-state phase diagram and magnetization process using DMRG and ED methods. It is shown that the zero-temperature magnetization curve may involve up to four intermediate plateaus at zero, one-fifth, two-fifth and three-fifth of the saturation magnetization, while the specific heat exhibits a striking low-temperature peak in a vicinity of discontinuous quantum phase transitions.