Related papers: Hyperbolic band theory
Photonic crystals are periodic structures which prevent light propagation along one or more directions in certain frequency intervals. Their band spectrum is usually analyzed using Floquet-Bloch decomposition. This spectrum is located on…
While the Bloch spectrum of translationally invariant noninteracting lattice models is trivially obtained by a Fourier transformation, diagonalizing the same problem in the presence of open boundary conditions is typically only possible…
We compute the phase diagram of the one-dimensional Bose-Hubbard model with a quasi-periodic potential by means of the density-matrix renormalization group technique. This model describes the physics of cold atoms loaded in an optical…
Onsite gain-loss-induced topological braiding principle of non-Hermitian energy bands is theoretically formulated in multiband lattice models with Hermitian hopping amplitudes. Braid phase transition occurs when the gain-loss parameter is…
Hyperbolic buildings are central objects in both hyperbolic geometry and geometric group theory, exhibiting a wide range of intriguing characteristics, especially with respect to group actions. In this paper, we develop the theory of…
In condensed-matter physics, long-range correlations introduce quantum states of matter that challenge intuition. For instance, supersolids combine symmetry-breaking crystalline structure, i.e. density order, and frictionless superfluid…
Solid-like behavior at low energies and long distances is usually associated with the spontaneous breaking of spatial translations at microscopic scales, as in the case of a lattice of atoms. We exhibit three quantum field theories that are…
The motion of a quantum system subjected to an external force often defeats our classical intuition. A celebrated example is the dynamics of a single particle in a periodic potential, which undergoes Bloch oscillations under the action of a…
For each stratum of the space of translation surfaces, we introduce an infinite translation surface containing in an appropriate manner a copy of every translation surface of the stratum. Given a translation surface $(X, \omega)$ in the…
Natural hyperbolic materials have attracted significant interest in the field of photonics due to their unique optical properties. Based on the initial successful explorations on layered crystalline materials, hyperbolic dispersion was…
The energy and structure of planar Bloch domain walls with opposite directions (right- and left-handed) and different paths of magnetization vector rotation have been systemized. The theory covers arbitrary oriented plates of cubic m3m…
Reduced Bloch mode expansion is presented for fast periodic media band structure calculations. The expansion employs a natural basis composed of a selected reduced set of Bloch eigenfunctions. The reduced basis is selected within the…
In a semiconductor superlattice with long scattering times, damping of Bloch oscillations due to scattering is so small that nonlinearities may compensate it and Bloch oscillations persist even in the hydrodynamic regime. To demonstrate…
Nonlinear theories generalizing Maxwell's electromagnetism and arising from a Lagrangian formalism have dispersion relations in which propagation planes factor into null planes corresponding to two effective metrics which depend on the…
Discontinuous quantum phase transitions and the associated metastability play central roles in diverse areas of physics ranging from ferromagnetism to false vacuum decay in the early universe. Using strongly-interacting ultracold atoms in…
We analyze surface electromagnetic waves with hyperbolic dispersion supported at the interface between a semi-infinite isotropic medium and an effective uniaxial material. Apart from known types plasmons with hyperbolic dispersion curve,…
Here, we reveal our recent progress on a geometrical approach of quantum physics and topological crystals linking with Dirac magnetic monopoles and gauge fields through classical electrodynamics. The Bloch sphere of a quantum spin-1/2…
Relations between particle and wave properties for charge carriers in periodic potentials of crystalline metals and semiconductors are derived. The particle aspects of electrons and holes in periodic potentials are considered using…
Semiclassical dynamics of Bloch electrons in a crystal under slowly varying deformation is developed in the geometric language of a lattice bundle. Berry curvatures and gradients of energy are introduced in terms of lattice covariant…
Standing wave patterns that arise on the surface of ferrofluids by (single frequency) parametric forcing with an ac magnetic field are investigated experimentally. Depending on the frequency and amplitude of the forcing, the system exhibits…