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The interplay of dynamical correlations and electronic ordering is pivotal in shaping phase diagrams of correlated quantum materials. In magic-angle twisted bilayer graphene, transport, thermodynamic, and spectroscopic experiments pinpoint a competition between distinct low-energy states with and without electronic order, as well as between localized and delocalized charge carriers. In this study, we utilize dynamical mean-field theory on the topological heavy fermion model of twisted bilayer graphene to investigate the emergence of electronic correlations and long-range order in the absence of strain. We contrast moment formation, Kondo screening, and ordering on a temperature basis and explain the nature of emergent correlated states based on three central phenomena: (i) the formation of local spin and valley isospin moments around 100 K, (ii) the ordering of the local isospin moments around 10 K preempting Kondo screening, and (iii) a cascadic redistribution of charge between localized and delocalized electronic states upon doping. At integer fillings, we find that low-energy spectral weight is depleted in the symmetric phase, while we find insulating states with gaps enhanced by exchange coupling in the zero-strain ordered phases. Doping away from integer filling results in distinct metallic states: a “bad metal” above the ordering temperature, where scattering off the disordered local moments suppresses electronic coherence, and a “good metal” in the ordered states with coherence of quasiparticles facilitated by isospin order. This finding reveals coherence from order as the microscopic mechanism behind the Pomeranchuk effect observed experimentally by Rozen et al. [Nature (London) 592, 214 (2021)NATUAS0028-083610.1038/s41586-021-03319-3] and by Saito et al. [Nature (London) 592, 220 (2021)NATUAS0028-083610.1038/s41586-021-03409-2]. Upon doping, there is a periodic charge reshuffling between localized and delocalized electronic orbitals leading to cascades of doping-induced Lifshitz transitions, local spectral weight redistributions, and periodic variations of the electronic compressibility ranging from nearly incompressible to negative. Our findings highlight the essential role of charge transfer, hybridization, and ordering in shaping the electronic excitations and thermodynamic properties in twisted bilayer graphene and provide a unified understanding of the most puzzling aspects of scanning tunneling spectroscopy, transport, and compressibility experiments.

We investigate the real-space profile of effective Coulomb interactions in correlated kagome materials. By particularizing to KV_{3}Sb_{5}, Co_{3}Sn_{2}S_{2}, FeSn, and Ni_{3}In, we analyze representative cases that exhibit a large span of correlation-mediated phenomena, and contrast them to prototypical perovskite transition metal oxides. From our constrained random phase approximation studies we find that the on-site interaction strength in kagome metals not only depends on the screening processes at high energy, but also on the low-energy hybridization profile of the electronic density of states. Our results indicate that rescaled by the on-site interaction amplitude, all kagome metals exhibit a universal long-range Coulomb behavior.

First-principles calculations of phonons are often based on the adiabatic approximation and on Brillouin-zone samplings that might not always be sufficient to capture the subtleties of Kohn anomalies. These shortcomings can be addressed through corrections to the phonon self-energy arising from the low-energy electrons. The exact self-energy involves a product of a bare and a screened electron-phonon vertex [Rev. Mod. Phys. 89, 015003 (2017)RMPHAT0034-686110.1103/RevModPhys.89.015003]; still, calculations often employ two adiabatically screened vertices, which have been proposed as a reliable approximation for self-energy differences [Phys. Rev. B 82, 165111 (2010)PRBMDO1098-012110.1103/PhysRevB.82.165111]. We assess the accuracy of both approaches in estimating the phonon spectral functions of model Hamiltonians and the adiabatic low-temperature phonon dispersions of monolayer TaS_{2} and doped MoS_{2}. We find that the approximate method yields excellent corrections at low computational cost, due to its designed error cancellation to first order, while using a bare vertex could in principle improve these results but is challenging in practice. We offer an alternative strategy based on downfolding to partially screened phonons and interactions [Phys. Rev. B 92, 245108 (2015)PRBMDO1098-012110.1103/PhysRevB.92.245108]. This is a natural scheme to include electron-electron interactions and tackle phonons in strongly correlated materials and the frequency dependence of the electron-phonon vertex.

Charge-density waves are responsible for symmetry-breaking displacements of atoms and concomitant changes in the electronic structure. Linear response theories, in particular density-functional perturbation theory, provide a way to study the effect of displacements on both the total energy and the electronic structure based on a single ab initio calculation. In downfolding approaches, the electronic system is reduced to a smaller number of bands, allowing for the incorporation of additional correlation and environmental effects on these bands. However, the physical contents of this downfolded model and its potential limitations are not always obvious. Here, we study the potential-energy landscape and electronic structure of the Su-Schrieffer-Heeger (SSH) model, where all relevant quantities can be evaluated analytically. We compare the exact results at arbitrary displacement with diagrammatic perturbation theory both in the full model and in a downfolded effective single-band model, which gives an instructive insight into the properties of downfolding. An exact reconstruction of the potential-energy landscape is possible in a downfolded model, which requires a dynamical electron-biphonon interaction. The dispersion of the bands upon atomic displacement is also found correctly, where the downfolded model by construction only captures spectral weight in the target space. In the SSH model, the electron-phonon coupling mechanism involves exclusively hybridization between the low- and high-energy bands and this limits the computational efficiency gain of downfolded models.