Related papers: Tile Hamiltonians for Decagonal Phases
An h-tiling on a finite simplicial complex is a partition of its geometric realization by maximal simplices deprived of several codimension one faces together with possibly their remaining face of highest codimension. In this last case, the…
In materials, certain approximated symmetry operations can exist in a lower-order approximation of the effective model but are good enough to influence the physical responses of the system, and these approximated symmetries were recently…
We use molecular dynamics simulations to study the driven phases of particles such as vortices or colloids moving over a decagonal quasiperiodic substrate. In the regime where the pinned states have quasicrystalline ordering, the driven…
Square-root topological phases have been discussed mainly for systems with chiral symmetry. In this paper, we analyze the topology of the squared Hamiltonian for systems preserving the time-reversal and particle-hole symmetry. Our analysis…
Topological crystalline insulators (TCI) possess electronic states protected by crystal symmetries, rather than time-reversal symmetry. We show that the transition metal oxides with heavy transition metals are able to support nontrivial…
We extend to the semi-classical setting the Maupertuis-Jacobi correspondance for a pair of hamiltonians $(H(x,hD_x), {\cal H}(x,hD_x)$. If ${\cal H}(p,x)$ is completely integrable, or has merely has invariant diohantine torus $\Lambda$ in…
Our understanding of physical properties of quasicrystals owes a great deal to studies of tight-binding models constructed on quasiperiodic tilings. Among the large number of possible quasiperiodic structures, two dimensional tilings are of…
Topological band insulators which are dynamically generated by electron-electron interactions have been the- oretically proposed in two and three dimensional lattice models. We present evidence that the two-dimensional version can be…
Fractional topological insulators (FTI) are electronic topological phases in $(3+1)$ dimensions enriched by time reversal (TR) and charge $U(1)$ conservation symmetries. We focus on the simplest series of fermionic FTI, whose bulk…
Corner states (CSs) in higher-order topological insulators (HOTIs) have recently been of great interest in both crystals and quasicrystals. In contrast to electronic systems, HOTIs have not been found in photonic quasicrystals (PQCs). Here,…
The U(1) Calogero-Sutherland Model with anti-periodic boundary condition is studied. This model is obtained by applying a vertical magnetic field perpendicular to the plane of one dimensional ring of particles. The trigonometric form of the…
A new kind of aperiodic tiling is introduced. It is shown to underlie a structure obtained as a superposition of waves with incommensurate periods. Its connections to other other tilings and quasicrystals are discussed.
Three-dimensional icosahedral random tilings with rhombohedral cells are studied in the semi-entropic model. We introduce a global energy measure defined by the variance of the quasilattice points in the orthogonal space. The internal…
Recently, the studies of topological corner states (TCSs) are extended from crystals to quasicrystals, which are referred to as higher-order topological quasicrystalline insulators (HOTQIs). However, the TCSs of complete quasi-periodic…
The strict geometric rules that define aperiodic tilings lead to the unique spectral and transport properties of quasicrystals, but also limit our ability to design them. In this Letter, we explore a novel example of a continuously tunable…
Altermagnetism, a novel magnetic phase characterized by symmetry-protected, momentum-dependent spin splitting and collinear compensated magnetic moments, has thus far been explored primarily in periodic crystals. In this Letter, we extend…
Metasurface, a kind of two-dimensional structured medium, represents a novel platform to manipulate the propagation of light at subwavelength scale. In linear optical regime, many interesting topics such as planar metalens, metasurface…
Expanding the library of self-assembled superstructures provides insight into the behavior of atomic crystals and supports the development of materials with mesoscale order. Here we build upon recent findings of soft matter quasicrystals…
Stoquastic Hamiltonians are characterized by the property that their off-diagonal matrix elements in the standard product basis are real and non-positive. Many interesting quantum models fall into this class including the Transverse field…
We propose a new example of discrete holography that provides a new step towards establishing the AdS/CFT duality for discrete spaces. A class of boundary Hamiltonians is obtained in a natural way from regular tilings of the hyperbolic…