Higher-order topological Mott insulator on the pyrochlore lattice

Higher-Order Topological Peierls Insulator in a Two-Dimensional Atom-Cavity System

In this work, we investigate a two-dimensional system of ultracold bosonic atoms inside an optical cavity, and show how photon-mediated interactions give rise to a plaquette-ordered bond pattern in the atomic ground state. The latter corresponds to a 2D Peierls transition, generalizing the spontaneous bond dimerization driven by phonon-electron interactions in the 1D Su-Schrieffer-Heeger (SSH) model. Here the bosonic nature of the atoms plays a crucial role to generate the phase, as similar generalizations with fermionic matter do not lead to a plaquette structure. Similar to the SSH model, we show how this pattern opens a nontrivial topological gap in 2D, resulting in a higher-order topological phase hosting corner states, that we characterize by means of a many-body topological invariant and through its entanglement structure. Finally, we demonstrate how this higher-order topological Peierls insulator can be readily prepared in atomic experiments through adiabatic protocols. Our work thus shows how atomic quantum simulators can be harnessed to investigate novel strongly correlated topological phenomena beyond those observed in natural materials.

Modification of topological corner excitations at the interplay of boundary geometry and Coulomb interaction

The effect of Coulomb interaction on the 2D second order topological superconductor is investigated taking into account different geometries of the boundary in the mainframe of the mean-field approximation. The spontaneous symmetry breaking, described earlier in Aksenovet al(2023Phys. Rev.B107125401), is found to be robust against the boundary deformation. Meanwhile, the details of the state with spontaneously broken symmetry is found to be dependent on the specific boundary geometry. Considering different types of the boundary of the 2D system, it is demonstrated that the deviation of the electron density in the broken symmetry state is determined by the position of the zero-dimensional (second-order) excitations with nearly zero energy. The critical value of the Coulomb interaction, at which the transition occurs, is found to be determined by the energy of these excitations, which is non-zero due to overlapping of the wave-functions at different corners.

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.