Javad Vahedi, Robert Peters, Ahmed Missaoui, Andreas Honecker, Guy Trambly de Laissardière
SciPost Phys. 11, 083 (2021) ·
published 27 October 2021
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We investigate magnetic instabilities in charge-neutral twisted bilayer graphene close to so-called "magic angles" using a combination of real-space Hartree-Fock and dynamical mean-field theories. In view of the large size of the unit cell close to magic angles, we examine a previously proposed rescaling that permits to mimic the same underlying flat minibands at larger twist angles. We find that localized magnetic states emerge for values of the Coulomb interaction $U$ that are significantly smaller than what would be required to render an isolated layer antiferromagnetic. However, this effect is overestimated in the rescaled system, hinting at a complex interplay of flatness of the minibands close to the Fermi level and the spatial extent of the corresponding localized states. Our findings shed new light on perspectives for experimental realization of magnetic states in charge-neutral twisted bilayer graphene.
Arne Schobert, Jan Berges, Tim Wehling, Erik van Loon
SciPost Phys. 11, 079 (2021) ·
published 20 October 2021
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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.
Eduardo Gonzalez Lazo, Markus Heyl, Marcello Dalmonte, Adriano Angelone
SciPost Phys. 11, 076 (2021) ·
published 13 October 2021
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We study the phase diagram and critical properties of quantum Ising chains with long-range ferromagnetic interactions decaying in a power-law fashion with exponent $\alpha$, in regimes of direct interest for current trapped ion experiments. Using large-scale path integral Monte Carlo simulations, we investigate both the ground-state and the nonzero-temperature regimes. We identify the phase boundary of the ferromagnetic phase and obtain accurate estimates for the ferromagnetic-paramagnetic transition temperatures. We further determine the critical exponents of the respective transitions. Our results are in agreement with existing predictions for interaction exponents $\alpha > 1$ up to small deviations in some critical exponents. We also address the elusive regime $\alpha < 1$, where we find that the universality class of both the ground-state and nonzero-temperature transition is consistent with the mean-field limit at $\alpha = 0$. Our work not only contributes to the understanding of the equilibrium properties of long-range interacting quantum Ising models, but can also be important for addressing fundamental dynamical aspects, such as issues concerning the open question of thermalization in such models.
