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

Figures (10)

• Figure 1: Conventional unit cells of $\mathrm{Sr_2CuO_3}$ (first), $\mathrm{SrBaCuO_3}$ (second), $\mathrm{Ba_2CuO_3}$ (third), $\mathrm{Sr_2CuO_{3.5}}$ (fourth), and $\mathrm{SrCuO_2}$ (fifth). In the first three materials, the Cu-O chains run along the crystallographic $a$ direction. In $\mathrm{Sr_2CuO_{3.5}}$, the Cu-O network forms a ladder structure located in the $ac$ plane, whereas in $\mathrm{SrCuO_2}$ the ladder lies in the $ab$ plane.
• Figure 2: The interchain Hubbard interactions $t_\perp$ and $V_\perp$ are replaced by an effective Heisenberg exchange $J_\perp$. Here $t$ and $U$ denote the intrachain hopping and on-site Coulomb interaction, while $t_\perp$, $V_\perp$, and $J_\perp$ describe interchain hopping, interchain Coulomb interaction, and spin exchange, respectively.
• Figure 3: The nearest neighbor chains are replaced by an effective MF with the staggered magnetization $M_s$ as parameter. Here $t$ and $U$ denote the intrachain hopping and on-site Coulomb interaction, while $J_\perp$ describes spin exchange.
• Figure 4: Schematic illustration of the MPS + MF framework, depicting the mapping from a lattice of coupled ladders to an effective single-ladder description. All intra- and interladder hopping processes included in the model are indicated.
• Figure 5: The electronic band structure of $\mathrm{Sr_2CuO_3}$, relative to the Fermi energy $E_F$. The striped black lines represent the Wannier interpolated bands. An orthorhombic supercell containing eight formula units has been used. The high-symmetry points of the Brillouin zone are labeled as $\Gamma=(0,0,0)$, $X=(0.5,0,0)$, $M=(0.5,0,0.5)$, $Z=(0,0,0.5)$ and $Y=(0,0.5,0)$.