Recently, superconductivity with a $T_c$ up to 78 K has been reported in bulk samples of the bilayer nickelate ${\mathrm{La}}_3{\text{Ni}}_2{\mathrm{O}}_7$ at pressures above 14 GPa. Important theoretical tasks are the formulation of relevant low-energy models and the clarification of the normal state properties. Here, we study the correlated electronic structure of the high-pressure phase in a four-orbital low-energy subspace using different many-body approaches: $GW$, dynamical mean field theory (DMFT), extended DMFT (EDMFT) and $GW+\mathrm{EDMFT}$, with realistic frequency-dependent interaction parameters. The nonlocal correlation and screening effects captured by $GW+\mathrm{EDMFT}$ result in an instability toward the formation of charge stripes, with the $3d_{z^2}$ as the main active orbital. We also comment on the potential relevance of the rare-earth self-doping pocket, since hole doping suppresses the ordering tendency.

Orbital polarization and Berry curvature signatures are mapped out by circular dichroism in angle-resolved photoemission.

Metal-insulator transitions in the paramagnetic phase of the two-dimensional square-lattice Hubbard model are studied using the dynamical cluster approximation with eight momentum cells. We show that both the interaction-driven and the doping-driven transitions are multistage and momentum-sector specific with Fermi-liquid metal and fully gapped insulator phases separated by an intermediate phase, in which some regions of the Brillouin zone are gapped while others sustain gapless quasiparticles. We argue that this is the coarse-grained version of a gradually shrinking arc or pocket. A pronounced particle-hole asymmetry is found.

The correlation functions of quantum systems—central objects in quantum field theories—are defined in high-dimensional space-time domains. Their numerical treatment thus suffers from the curse of dimensionality, which hinders the application of sophisticated many-body theories to interesting problems. Here, we propose a multiscale space-time ansatz for correlation functions of quantum systems based on quantics tensor trains (QTTs), “qubits” describing exponentially different length scales. The ansatz then assumes a separation of length scales by decomposing the resulting high-dimensional tensors into tensor trains (also known as matrix product states). We numerically verify the ansatz for various equilibrium and nonequilibrium systems and demonstrate compression ratios of several orders of magnitude for challenging cases. Essential building blocks of diagrammatic equations, such as convolutions or Fourier transforms, are formulated in the compressed form. We numerically demonstrate the stability and efficiency of the proposed methods for the Dyson and Bethe-Salpeter equations. The QTT representation provides a unified framework for implementing efficient computations of quantum field theories.

Pumping graphene with circularly polarized light is the archetype of light-tailoring topological bands. Realizing the induced Floquet-Chern-insulator state and demonstrating clear experimental evidence for its topological nature has been a challenge, and it has become clear that scattering effects play a crucial role. We tackle this gap between theory and experiment by employing microscopic quantum kinetic calculations including realistic electron-electron and electron-phonon scattering. Our theory provides a direct link to the build up of the Floquet-Chern-insulator state in light-driven graphene and its detection in time- and angle-resolved photoemission spectroscopy (ARPES). This approach allows us to study the robustness of the Floquet features against dephasing and thermalization effects. We also discuss the ultrafast Hall response in the laser-heated state. Furthermore, the induced pseudospin texture and the associated Berry curvature give rise to momentum-dependent orbital magnetization, which is reflected in circular dichroism in ARPES (CD-ARPES). Combining our nonequilibrium calculations with an accurate one-step theory of photoemission allows us to establish a direct link between the build up of the topological state and the dichroic pump-probe photoemission signal. The characteristic features in CD-ARPES are shown to be stable against heating and dephasing effects. Thus, tracing circular dichroism in time-resolved photoemission provides new insights into transient topological properties.