Higher-order topological insulator in a modified Haldane-Hubbard model

We investigate the ground-state phase diagram of a modified spinless Haldane-Hubbard model with broken threefold rotational symmetry, employing exact diagonalization calculations. The interplay of asymmetry, interactions, and topology gives rise to a rich phase diagram. The non-interacting limit of the Hamiltonian exhibits a higher-order topological insulator characterized by the existence of corner modes, in contrast to known chiral edge metallic states of the standard Haldane model. Our investigation demonstrates that these symmetry-protected states are robust to the presence of finite interactions. Furthermore, in certain regimes of parameters, we show that a topological Mott insulator exists in this model, where a non-trivial topological bulk coexists with an interaction-driven charge-density-wave, whose emergence is characterized by a $Z_2$-symmetry breaking within the 3$d$-Ising universality class.Comment: 9 pages, 9 figure

Dimensionless ratios: characteristics of quantum liquids and their phase transitions

Dimensionless ratios of physical properties can characterize low-temperature phases in a wide variety of materials. As such, the Wilson ratio (WR), the Kadowaki-Woods ratio and the Wiedemann\--Franz law capture essential features of Fermi liquids in metals, heavy fermions, etc. Here we prove that the phases of many-body interacting multi-component quantum liquids in one dimension (1D) can be described by WRs based on the compressibility, susceptibility and specific heat associated with each component. These WRs arise due to additivity rules within subsystems reminiscent of the rules for multi-resistor networks in series and parallel --- a novel and useful characteristic of multi-component Tomonaga-Luttinger liquids (TLL) independent of microscopic details of the systems. Using experimentally realised multi-species cold atomic gases as examples, we prove that the Wilson ratios uniquely identify phases of TLL, while providing universal scaling relations at the boundaries between phases. Their values within a phase are solely determined by the stiffnesses and sound velocities of subsystems and identify the internal degrees of freedom of said phase such as its spin-degeneracy. This finding can be directly applied to a wide range of 1D many-body systems and reveals deep physical insights into recent experimental measurements of the universal thermodynamics in ultracold atoms and spins.Comment: 12 pages (main paper), (6 figures

Nonlinear optomechanical resonance entering a self-organized energy transfer pattern

The energy transfer between different subsystems or different vibration modes is always one of the most interested problems in the study of the resonance phenomena in coupled nonlinear dynamical systems. With an optomechanical system operating in the regime of unresolved sideband, where its mechanical frequency is lower than the cavity field damping rate, we illustrate the existence of a special nonlinear resonance phenomenon. This type of previously unknown resonance manifests an organized pattern of the coupled cavity field and mechanical oscillation, so that the cavity field precisely pushes the mechanical oscillator within an appropriate small time window in each mechanical oscillation period and the mechanical energy will increase by a jump of almost fixed amount after each oscillation cycle. The scenario is realized at a resonance point where the frequency difference of two driving fields matches the mechanical frequency of the system, and this condition of drive-frequency match is found to trigger a mechanism to lock the two subsystems of an unresolved-sideband optomechanical system into a highly ordered energy transfer as the above mentioned. Due to a significantly enhanced nonlinearity in the vicinity of the resonance point, optical frequency combs can be generated under pump powers of thousand times lower, as compared to the use of a single-tone driving field for the purpose. An unresolved sideband system under the drives without satisfying the resonance condition also demonstrates other interesting dynamical behaviors. Most of all, by providing a realistic picture for the nonlinear optomechanical dynamics in unresolved sideband regime, our study points to a direction to observe novel dynamical phenomena and realize other applications with the systems of less technical restrictions.Comment: 13 pages, 13 figures. To be published on Chaos, Solitons & Fractal

Towards a temporal network analysis of interactive WiFi users

Complex networks are used to depict topological features of complex systems. The structure of a network characterizes the interactions among elements of the system, and facilitates the study of many dynamical processes taking place on it. In previous investigations, the topological infrastructure underlying dynamical systems is simplified as a static and invariable skeleton. However, this assumption cannot cover the temporal features of many time-evolution networks, whose components are evolving and mutating. In this letter, utilizing the log data of WiFi users in a Chinese university campus, we infuse the temporal dimension into the construction of dynamical human contact network. By quantitative comparison with the traditional aggregation approach, we find that the temporal contact network differs in many features, e.g., the reachability, the path length distribution. We conclude that the correlation between temporal path length and duration is not only determined by their definitions, but also influenced by the microdynamical features of human activities under certain social circumstance as well. The time order of individuals' interaction events plays a critical role in understanding many dynamical processes via human close proximity interactions studied in this letter. Besides, our study also provides a promising measure to identify the potential superspreaders by distinguishing the nodes functioning as the relay hub.Comment: 6 pages, 6 figure