Combining matrix product states and mean-field theory to capture magnetic order in quasi-1D cuprates

TL;DR

This paper combines tensor-network simulations and mean-field theory to model magnetic order in quasi-1D cuprates, successfully reconciling theoretical predictions with experimental observations.

Contribution

It introduces a multi-step approach integrating density functional theory, downfolding, tensor networks, and mean-field theory to accurately describe magnetic order in quasi-1D cuprates.

Findings

Purely 1D models lack long-range magnetic order.

Incorporating interchain couplings stabilizes magnetic order.

The approach aligns well with experimental results for certain cuprates.

Abstract

We study quasi-one-dimensional strongly correlated materials using a multi-step approach based on density functional theory, downfolding techniques, and tensor-network simulations. The downfolding procedure yields effective multiband Hubbard models that capture the competition between electron hopping and local Coulomb interactions relevant to the system's low-energy properties. The resulting multiband Hubbard models are solved using matrix product states. Applied to Sr$_2$CuO$_3$, SrBaCuO$_3$, and Ba$_2$CuO$_3$, this purely one-dimensional treatment yields no long-range magnetic order, in contrast to the magnetic ordering observed experimentally. To account for this behavior, we extend the multi-step approach by incorporating interchain couplings through a self-consistent mean-field scheme. This combined approach stabilizes finite staggered magnetizations, providing a consistent description of magnetic order in agreement with experiment. For Sr$_2$CuO$_{3.5}$ and SrCuO$_2$, we also tested an approach proposed for ladder materials, however, we find that these materials are not well suited for this approach due to the small magnitude of the intraladder hopping parameters.