Moiré band renormalization due to lattice mismatch in bilayer graphene.

We investigated the band renormalization caused by the compressive-strain-induced lattice mismatch in parallel AA stacked bilayer graphene using two complementary methods: the tight-binding approach and the low-energy continuum theory. While a large mismatch does not alter the low-energy bands, a small one reduces the bandwidth of the low-energy bands along with a decrease in the Fermi velocity. In the tiny-mismatch regime, the low-energy continuum theory reveals that the long-period moiré pattern extensively renormalizes the low-energy bands, resulting in a significant reduction of bandwidth. Meanwhile, the Fermi velocity exhibits an oscillatory behavior and approaches zero at specific mismatches. However, the resulting low-energy bands are not perfectly isolated flat, as seen in twisted bilayer graphene at magic angles. These findings provide a deeper understanding of moiré physics and offer valuable guidance for related experimental studies in creating moiré superlattices using two-dimensional van der Waals heterostructures.

Quantum phase transitions of interacting bosons on hyperbolic lattices.

The effect of many-body interaction in curved space is studied based on the extended Bose-Hubbard model on hyperbolic lattices. Using the mean-field approximation and quantum Monte Carlo simulation, the phase diagram is explicitly mapped out, which contains the superfluid, supersolid and insulator phases at various fillings. Particularly, it is revealed that the sizes of the Mott lobes shrink and the supersolid is stabilized at smaller nearest-neighbor interaction asqin the Schläfli symbol increases. The underlying physical mechanism is attributed to the increase of the coordination number, and hence the kinetic energy and the nearest-neighbor interaction. The results suggest that the hyperbolic lattices may be a unique platform to study the effect of the coordination number on quantum phase transitions, which may be relevant to the experiments of ultracold atoms in optical lattices.

Quantum Monte Carlo study of topological phases on a spin analogue of Benalcazar-Bernevig-Hughes model.

We study the higher-order topological spin phases based on a spin analogue of Benalcazar-Bernevig-Hughes model in two dimensions using large-scale quantum Monte Carlo simulations. A continuous Néel-valence bond solid quantum phase transition is revealed by tuning the ratio between dimerized spin couplings, namely, the weak and strong exchange couplings. Through the finite-size scaling analysis, we identify the phase critical points, and consequently, map out the full phase diagrams in related parameter spaces. Particularly, we find that the valence bond solid phase can be a higher-order topological spin phase, which has a gap for spin excitations in the bulk while demonstrates characteristic gapless spin modes at corners of open lattices. We further discuss the connection between the higher-order topological spin phases and the electronic correlated higher-order phases, and find both of them possess gapless spin corner modes that are protected by higher-order topology. Our result exemplifies higher-order physics in the correlated spin systems and will contribute to further understandings of the many-body higher-order topological phenomena.

Quantum magnetism of topologically-designed graphene nanoribbons.

Based on the Hubbard models, quantum magnetism of topologically-designed graphene nanoribbons (GNRs) is studied using exact numerical simulations. We first study a two-band Hubbard model describing the low-energy topological bands using the density matrix renormalization group (DMRG) and determinant quantum Monte Carlo (DQMC) methods. It is found the spin correlations decay quickly with distance, and the local moment is extrapolated to zero in the presence of symmetry-breaking terms. The results show that the two-band Hubbard chain is nonmagnetic, which is in contrast to the mean-field calculation predicting a critical interaction for the magnetic transition. We then include the Hubbard interaction to the topological-designed GNRs. For large interactions, the spin correlations remain finite for all distances, and the magnetic order develops. The local moment is extrapolated to almost zero for weak interactions, and begins to increase rapidly from a critical interaction. The estimated critical value is much larger than the realistic value in graphene, and we conclude the experimentally relevant GNRs are nonmagnetic, which is consistent with the experimental results.