# Electronic structure and magnetic properties of Li_2ZrCuO_4 - a spin 1/2 Heisenberg system in vicinity to a quantum critical point

## TL;DR

This study uses density functional theory to analyze the electronic and magnetic properties of Li_2ZrCuO_4, revealing its proximity to a quantum critical point and the effects of structural features on magnetic interactions.

## Contribution

It provides a detailed theoretical analysis of Li_2ZrCuO_4's electronic structure and magnetic interactions near a quantum critical point, incorporating structural disorder and geometry effects.

## Key findings

- The ratio alpha = -J_2/J_1 is approximately 0.22, close to the critical point at 1/4.
- Structural peculiarities influence magnetic interactions significantly.
- Optical conductivity shows strong temperature dependence predicted by Hubbard model simulations.

## Abstract

Based on density functional calculations, we present a detailed theoretical study of the electronic structure and the magnetic properties of the quasi-one dimensional chain cuprate Li_2ZrCuO_4 (Li_2CuZrO_4). For the relevant ratio of the next-nearest neighbor exchange J_2 to the nearest neighbor exchange J_1 we find alpha = -J_2/J_1 = 0.22\pm0.02 which is very close to the critical point at 1/4. Owing this vicinity to a ferromagnetic-helical critical point, we study in detail the influence of structural peculiarities such as the reported Li disorder and the non-planar chain geometry on the magnetic interactions combining the results of LDA based tight-binding models with LDA+U derived exchange parameters. Our investigation is complemented by an exact diagonalization study of a multi-band Hubbard model for finite clusters predicting a strong temperature dependence of the optical conductivity for Li_2ZrCuO_4.