Related papers: Bloch classification surface for three-band system…
Scattering problems with locally perturbed periodic surfaces have been studied both theoretically and numerically in recent years. In this paper, we will discuss the regularity results of the Bloch transform of the total fields. The idea is…
We study separability criteria in multipartite quantum systems of arbitrary dimensions by using the Bloch representation of density matrices. We first derive the norms of the correlation tensors and obtain the necessary conditions for…
Topological band insulators (TBIs) are bulk insulating materials which feature topologically protected metallic states on their boundary. The existing classification departs from time-reversal symmetry, but the role of the crystal lattice…
We study the genuine multipartite entanglement in tripartite quantum systems. By using the Schmidt decomposition and local unitary transformation, we convert the general states to simpler forms and consider certain matrices from correlation…
We use the bulk Hamiltonian for a three-dimensional topological insulator such as $\rm Bi_2 Se_3$ to study the states which appear on its various surfaces and along the edge between two surfaces. We use both analytical methods based on the…
The quantum confinement of Bloch waves is fundamentally different from the well-known quantum confinement of plane waves. Unlike that obtained in the latter are all stationary states only; in the former, there is always a new type of states…
We theoretically study the three-dimensional topological semimetals with nodal surfaces protected by crystalline symmetries. Different from the well-known nodal-point and nodal-line semimetals, in these materials, the conduction and valence…
Bloch wavefunctions are used to derive dispersion relations for water wave propagation in the presence of an infinite array of periodically arranged surface scatterers. For one dimensional periodicity (stripes), band gaps for wavevectors in…
In contrast to the usual bulk-boundary correspondence, topological states localized within the bulk of the system have been numerically identified in quasicrystalline structures, termed bulk localized transport (BLT) states. These states…
Here a generalised argument showing the existence of the Bloch superselection rule is presented, in response to the recent comment by Sowinski. In light of the role played by the periodic boundary condition, locality and topology in the…
We have given a novel formulation of the exact solutions for the lambda, vee and cascade three-level systems where the Hamiltonian of each configuration is expressed in the SU(3) basis. The solutions are discussed from the perspective of…
The vacuum of a band system, with respect to particles or holes, can become topologically nontrivial when the exceptional points of the non-hermitian Hamiltonian spread over the whole Brillouin zone. The coalescence of the eigenstates…
Topological insulators have gapless states at their boundaries while trivial insulators generically do not. We consider loops in the spaces of Hamiltonians of topologically trivial Bloch insulators, and show that there exist loops for which…
Topological insulators exhibit boundary states protected by bulk band topology, a principle first established in quantum systems and later extended to classical waves, including phononics. Conventionally, an $n$-dimensional bulk with…
Higher-order topological insulators are a new class of topological phases of matter, originally conceived for electrons in solids. It has been suggested that $\mathbb{Z}_N$ Berry phase (Berry phase quantized into $2\pi/N$) is a useful tool…
The properties of the geometric phases between three quantum states are investigated in a high-dimensional Hilbert space using the Majorana representation of symmetric quantum states. We found that the geometric phases between the three…
We study ``frustrated'' hopping models, in which at least one energy band, at the maximum or minimum of the spectrum, is dispersionless. The states of the flat band(s) can be represented in a basis which is fully localized, having support…
We show that, after a transformation, the dynamics of linear perturbations (spin waves) around a singular Bloch point soliton is formally equivalent to a quantum system of an electron in a magnetic monopole field. The analytical solution to…
We construct a coherent state path integral formalism for the one-dimensional Bloch particle within the single band model. The transition amplitude between two coherent states is a sum of transition amplitudes with different winding numbers…
An ability to describe quantum states directly by average values of measurement outcomes is provided by the Bloch vector. For an informationally complete set of measurements one can construct unique Bloch vector for any quantum state.…