Periodically driven systems provide tunable platforms to realize interesting Floquet topological phases and phase transitions. In electronic systems with Weyl dispersions, the band crossings are topologically protected even in the presence of time-periodic perturbations. This robustness permits various routes to shift and tilt the Weyl spectra in the momentum and energy space using circularly polarized light of sufficient intensity. We show that type-II Weyl fermions, in which the Weyl dispersions are tilted with the appearance of pocket-like Fermi surfaces, can be induced in driven Dirac semimetals and line node semimetals. Under a circularly polarized drive, both semimemtal systems immediately generate Weyl node pairs whose types can be further controlled by the driving amplitude and direction. The resultant phase diagrams demonstrate experimental feasibilities.

We construct Holstein-Primakoff Hamiltonian for magnons in arbitrary slowly varying spin background, for a microscopic spin Hamiltonian consisting of ferromagnetic spin exchange, Dzyaloshinskii-Moriya exchange, and the Zeeman term. The Gross-Pitaevskii-type equation for magnon dynamics contains several background gauge fields pertaining to local spin chirality, inhomogeneous potential, and anomalous scattering that violates the boson number conservation. Non-trivial corrections to previous formulas derived in the literature are given. Subsequent mapping to hydrodynamic fields yields the continuity equation and the Euler equation of the magnon fluid dynamics. Magnon wave scattering off a localized Skyrmion is examined numerically based on our Gross-Pitaevskii formulation. Dependence of the effective flux experienced by the impinging magnon on the Skyrmion radius is pointed out, and compared with analysis of the same problem using the Landau-Lifshitz-Gilbert equation.

A rank-2 toric code (R2TC) Hamiltonian in two dimensions can be constructed as a Higgsed descendant of rank-2 U(1) lattice gauge theory. As noted by the authors recently, [Y.-T. Oh, J. Kim, and J. H. Han, Phys. Rev. B 105, 045128] the quasiparticles in that model showed braiding statistics that depends on the initial locations of the particles which participate in the braiding. We argue that this new kind of statistical phase captures the total dipole moment of quasiparticles encompassed in the braiding, whereas conventional anyonic braiding sees the total charge. An Aharonov-Bohm interpretation of such dipolar braiding statistics can be made in terms of emergent, rank-1 vector potentials built from the underlying rank-2 gauge fields. Pertinent field theories of the quasiparticle dynamics in the R2TC are developed, which turn out to be highly interacting theories predicting their constrained dynamics. The accompanying conservation laws are also of unusual types. A dipolar BF theory of the rank-2 gauge fields is constructed and shown to correctly capture the dipolar braiding statistics, in contrast to the conventional BF theory capturing the monopolar braiding statistics of anyons in the rank-1 toric code. A tight-binding model for the quasiparticle dynamics in the R2TC involves two-particle as well as the one-particle hopping, both of which are coupled to the tensor gauge fields.

A new kind of spin-1 chain Hamiltonian consisting of competing dimer and trimer projection operators is proposed. As the relative strengths and signs of the interactions are varied, the model exhibits a number of different phases including the gapped dimer phase and the gapless trimer phase with critical correlations described by a conformal field theory with central charge c = 2. A symmetry-protected topological phase also exists in this model, even though the microscopic interactions are not the simple adiabatic extensions of the well-known Heisenberg and the AffleckKennedy-Lieb-Tasaki model and contains both two-and three-particle permutations. A fourth phase is characterized by macroscopically degenerate ground states. While bearing almost a oneto-one resemblance to the phase diagram of the bilinear-biquadratic spin-1 chain Hamiltonian, our model is rooted on very different physical origin, namely the two competing tendencies of spin-1 particles to form singlets through either dimer or trimer formation.

Based on first-principles calculations, we predict a new two-dimensional ferromagnetic material that exhibits exotic Fermi surface topology. We show that monolayer hexagonal indium carbide (h-InC) is thermodynamically and dynamically stable, and it energetically favors the ferromagnetic ordering of spins. The perfectly planar geometry in two dimensions, together with ferromagnetism, gives rise to a unique opportunity to encounter intriguing electronic properties, captured in the Fermi surface and band topology. We show that multiple nodal lines coexist in momentum space, accompanied by the electron and hole pockets that touch each other linearly at the nodal lines. Inclusion of spin-orbit coupling enriches the magnetic and electronic properties of h-InC. Spin-orbit coupling leads to an easy-plane type magnetocrystalline anisotropy, and the nodal lines can be tuned into topological nodal points, contingent upon the magnetization direction. Symmetry analysis and a tight-binding model are provided to explain the nodal structure of the bands. Our findings suggest h-InC as a new venue for supporting carbon-based magnetism and exotic band topology in two dimensions.