Interplay of Quantum Criticality and Geometric Frustration in Columbite

TL;DR

This paper explores the complex quantum phases arising from the interplay of quantum criticality and geometric frustration in columbite, specifically in CoNb2O6, revealing a rich phase diagram with five distinct states.

Contribution

It introduces a theoretical model combining exact chain solutions with perturbative methods to analyze quantum phases in a frustrated magnetic system.

Findings

Identification of five distinct quantum phases at zero temperature.

Discovery of quantum phase transitions between these phases.

Relevance of results to experimental observations in CoNb2O6.

Abstract

Motivated by CoNb2O6 (belonging to the columbite family of minerals), we theoretically study the physics of quantum ferromagnetic Ising chains coupled anti-ferromagnetically on a triangular lattice in the plane perpendicular to the chain direction. We combine exact solutions of the chain physics with perturbative approximations for the transverse couplings. When the triangular lattice has an isosceles distortion (which occurs in the real material), the T=0 phase diagram is rich with five different states of matter: ferrimagnetic, N\'eel, anti-ferromagnetic, paramagnetic and incommensurate phases, separated by quantum phase transitions. Implications of our results to experiments on CoNb2O6 are discussed.