Related papers: Scaled Tight-Binding Crystal
We study, analytically and numerically, a simple $\mathcal{PT}$-symmetric tight-binding ring with an onsite energy $a$ at the gain and loss sites. We show that if $a\neq 0$, the system generically exhibits an unbroken…
We study flat bands in bipartite tight-binding networks with discrete translational invariance. Chiral flat bands with chiral symmetry eigenenergy E = 0 and host compact localized eigenstates for finite range hopping. For a bipartite…
The density of states, even for a perfectly ordered tight-binding model, can exhibit a tail-like feature at the top of the band, provided the hopping integral falls off in space slowly enough. We apply the coherent potential approximation…
We report on a hitherto unnoticed type of resonances occurring in scattering from networks (quantum graphs) which are due to the complex connectivity of the graph - its topology. We consider generic open graphs and show that any cycle leads…
A connection between the dynamics of a sine-Gordon chain and a certain static membrane folding problem was recently found. The one-dimensional membrane profile is a cross-section of the position-time sine-Gordon amplitude profile. Here we…
We study the nonlinear wave dynamics of one-dimensional chains of polycatenated rings. These interlocked structures support amplitude-dependent nonlinear wave propagation driven by tensile activation and internal structural flexibility,…
Many-electron systems confined to a quasi-1D geometry by a cylindrical distribution of positive charge have been investigated by density functional computations in the unrestricted local spin density approximation. Our investigations have…
We formulate a theory for resonances in the many-body localised (MBL) phase of disordered quantum spin chains in terms of local observables. A key result is to show that there are universal correlations between the matrix elements of local…
Sample correlation matrices are employed ubiquitously in statistics. However, quite surprisingly, little is known about their asymptotic spectral properties for high-dimensional data, particularly beyond the case of "null models" for which…
We develop a variational formalism in order to study the structure of low energy spectra of frustrated quantum spin systems. It is first applied to trial wavefunctions of ladders with one spin-1/2 on each site. We determine energy minima of…
Spectroscopic measurements with low-temperature scanning tunneling microscopes have been used very successfully for studying not only individual atomic or molecular spins on surfaces but also complexly designed coupled systems. The symmetry…
We investigate the spectral and transport properties of a two-arm tight-binding ladder perturbed by an external magnetic field following an Aubry-Andr\'e-Harper profile. The varying magnetic flux trapped in consecutive ladder-cells…
The structure and degree of order in soft matter and other materials is intimately connected to the nature of the interactions between the particles. One important research goal is to find suitable control mechanisms, to enhance or suppress…
We calculate statistical properties of amorphous polymer chains between crystalline lamellae by self-consistent field model simulations. In our model, an amorphous subchain is modelled as a polymer chain of which ends are grafted onto the…
The self-assembly of functionalized (patchy) particles with directional interactions into target structures is still a challenge, despite the significant experimental advances on their synthesis. The self-assembly pathways are typically…
The fundamental concept underlying topological phenomena posits the geometric phase associated with eigenstates. In contrast to this prevailing notion, theoretical studies on time-varying Hamiltonians allow for a new type of topological…
We theoretically analyze a discrete Schr\"odinger chain with hopping to the first and second neighbors, as can be realized with zigzag arrangements of optical waveguides or lattice sites for cold atoms. Already at moderate values, the…
We introduce the concept of parity symmetry in restricted spatial domains -- local parity -- and explore its impact on the stationary transport properties of generic, one-dimensional aperiodic potentials of compact support. It is shown…
We investigate the spectral properties and dynamical features of a time-periodic PT-symmetric Hamiltonian on a one-dimensional tight-binding lattice. It is shown that a high-frequency modulation can drive the system under a transition…
We discuss the concept of discrete scale invariance and how it leads to complex critical exponents (or dimensions), i.e. to the log-periodic corrections to scaling. After their initial suggestion as formal solutions of renormalization group…