Motivated by recent experimental progress on iron-based ladder compounds, we study the doped two-orbital Hubbard model for the two-leg ladder BaFe$_2$S$_3$. The model is constructed by using {it ab initio} hopping parameters and the ground state prop
erties are investigated using the density matrix renormalization group method. We show that the $(pi,0)$ magnetic ordering at half-filling, with ferromagnetic rungs and antiferromagnetic legs, becomes incommensurate upon hole doping. Moreover, depending on the strength of the Hubbard $U$ coupling, other magnetic patterns, such as $(0,pi)$, are also stabilized. We found that the binding energy for two holes becomes negative for intermediate Hubbard interaction strength, indicating hole pairing. Due to the crystal-field split among orbitals, the holes primarily reside in one orbital, with the other one remaining half-filled. This resembles orbital selective Mott states. The formation of tight hole pairs continues with increasing hole density, as long as the magnetic order remains antiferromagnetic in one direction. The study of pair-pair correlations indicates the dominance of the intra-orbital spin-singlet channel, as opposed to other pairing channels. Although in a range of hole doping pairing correlations decay slowly, our results can also be interpreted as corresponding to a charge-density-wave made of pairs, a precursor of eventual superconductivity after interladder couplings are included. Such scenario of intertwined orders has been extensively discussed before in the cuprates, and our results suggest a similar physics could exist in ladder iron-based superconductors. Finally, we also show that a robust Hunds coupling is needed for pairing to occur.
Motivated by recent experimental progress in transition metal oxides with the K$_2$NiF$_4$ structure, we investigate the magnetic and orbital ordering in $alpha$-Sr$_2$CrO$_4$. Using first principles calculations, first we derive a three-orbital Hubb
ard model, which reproduces the {it ab initio} band structure near the Fermi level. The unique reverse splitting of $t_{2g}$ orbitals in $alpha$-Sr$_2$CrO$_4$, with the $3d^2$ electronic configuration for the Cr$^{4+}$ oxidation state, opens up the possibility of orbital ordering in this material. Using real-space Hartree-Fock for multi-orbital systems, we constructed the ground-state phase diagram for the two-dimensional compound $alpha$-Sr$_2$CrO$_4$. We found stable ferromagnetic, antiferromagnetic, antiferro-orbital, and staggered orbital stripe ordering in robust regions of the phase diagram. Furthermore, using the density matrix renormalization group method for two-leg ladders with the realistic hopping parameters of $alpha$-Sr$_2$CrO$_4$, we explore magnetic and orbital ordering for experimentally relevant interaction parameters. Again, we find a clear signature of antiferromagnetic spin ordering along with antiferro-orbital ordering at moderate to large Hubbard interaction strength. We also explore the orbital-resolved density of states with Lanczos, predicting insulating behavior for the compound $alpha$-Sr$_2$CrO$_4$, in agreement with experiments. Finally, an intuitive understanding of the results is provided based on a hierarchy between orbitals, with $d_{xy}$ driving the spin order, while electronic repulsion and the effective one dimensionality of the movement within the $d_{xz}$ and $d_{yz}$ orbitals driving the orbital order.
The magnetic and electronic phase diagram of a model for the quasi-one-dimensional alkali metal iron selenide compound Na$_2$FeSe$_2$ is presented. The novelty of this material is that the valence of iron is Fe$^{2+}$ contrary to most other iron-chai
n compounds with valence Fe$^{3+}$. Using first-principles techniques, we developed a three-orbital tight-binding model that reproduces the {it ab initio} band structure near the Fermi level. Including Hubbard and Hund couplings and studying the model via the density matrix renormalization group and Lanczos methods, we constructed the ground state phase diagram. A robust region where the block state $uparrow uparrow downarrow downarrow uparrow uparrow downarrow downarrow$ is stabilized was unveiled. The analog state in iron ladders, employing 2$times$2 ferromagnetic blocks, is by now well-established, but in chains a block magnetic order has not been observed yet in real materials. The phase diagram also contains a large region of canonical staggered spin order $uparrow downarrow uparrow downarrow uparrow downarrow uparrow$ at very large Hubbard repulsion. At the block to staggered transition region, a novel phase is stabilized with a mixture of both states: an inhomogeneous orbital-selective charge density wave with the exotic spin configuration $uparrow uparrow downarrow uparrow downarrow downarrow uparrow downarrow$. Our predictions for Na$_2$FeSe$_2$ may guide crystal growers and neutron scattering experimentalists towards the realization of block states in one-dimensional iron-selenide chain materials.
We discuss a protocol based on quenching a purified quantum system that allows to capture bulk spectral features. It uses an infinite temperature initial state and an interferometric strategy to access the Loschmidt amplitude, from which the spectral
features are retrieved via Fourier transform, providing coarse-grained approximation at finite times. It involves techniques available in current experimental setups for quantum simulation, at least for small systems. We illustrate possible applications in testing the eigenstate thermalization hypothesis and the physics of many-body localization.
