Quantum Rotors on the AB$_2$ Chain with Competing Interactions

TL;DR

This paper explores the phase diagram of quantum-rotor chains with competing interactions, comparing results from mean-field approaches to known spin-1/2 models and classical analogs, revealing insights into frustration-induced phenomena.

Contribution

It introduces a quantum-rotor model with competing interactions, providing a detailed comparison with spin-1/2 systems and classical models, and extends understanding of frustration effects in quantum chains.

Findings

Quantum-rotor phase diagrams show similarities to spin-1/2 models.

Mean-field approaches effectively capture key phase features.

Frustration induces magnon condensation phenomena.

Abstract

We present the ground state phase diagram of $q = 1/2$ quantum-rotor chains with competing interactions (frustration) calculated through cluster variational mean field approaches. We consider two interaction patterns, named F$_1$ and F$_2$ models, between the quantum-rotor momentum and position operators, which follow exchange patterns of known one-dimensional spin-1/2 systems with a ferrimagnetic state in their phase diagrams. The spin-1/2 F$_1$ model is known as the diamond chain and is related to the azurite compound, while the spin-1/2 F$_2$ model was recently shown to present a frustration-induced condensation of magnons. We provide a detailed comparison between the quantum-rotor phase diagrams, in single- and multi-site mean-field approaches, and known results for the spin-1/2 models, including exact diagonalization and density matrix renormalization group data for these systems, as well as phase diagrams of the associated classical models.