Condensed Matter

We present a numerical investigation of the density fluctuations in a model glass under cyclic shear deformation. At low amplitude of shear, below yielding, the system reaches a steady absorbing state in which density fluctuations are suppressed revealing a clear fingerprint of hyperuniformity up to a finite length scale. The opposite scenario is observed above yielding, where the density fluctuations are strongly enhanced. We demonstrate that the transition to this state is accompanied by a spatial phase separation into two distinct hyperuniform regions, as a consequence of shear band formation above the yield amplitude.

We present a numerical study on a disordered artificial spin-ice system which interpolates between the long-range ordered square ice and the fully degenerate shakti ice. Starting from the square-ice geometry, disorder is implemented by adding vertical/horizontal magnetic islands to the center of some randomly chosen square plaquettes of the array, at different densities. When no island is added we have ordered square ice. When all square plaquettes have been modified we obtain shakti ice, which is disordered yet in a topological phase corresponding to the Rys F-model. In between, geometrical frustration due to these additional center spins disrupts the long-range Ising order of square-ice, giving rise to a spin-glass regime at low temperatures. The artificial spin system proposed in our work provides an experimental platform to study the interplay between quenched disorder and geometrical frustration.

We performed all-atom molecular dynamics simulations for bulk cyclohexane and analysed the short- and medium-range structures in supercooled and glassy states by using the Voronoi tessellation technique. From the analyses of both the potential energy of the system and the radial distribution function of molecules, cyclohexane was found to be vitrified as the temperature decreased. Furthermore, the icosahedral-like structures are dominant at all temperatures and grow in a supercooled liquid, whereas the face-centred cubic structures do not grow when the temperature decreases. It was also ascertained that the icosahedral-like structure is more dominant than the full-icosahedral one. The network of the distorted icosahedron spreads throughout the system at low temperatures. Our simulation demonstrates the stability of the icosahedral structure even in a non-spherical molecule such as cyclohexane.

We have proposed and implemented a modification of the well-known wall follower algorithm to identify a backbone (a current-carrying part) of the percolation cluster. The advantage of the modified algorithm is identification of the whole backbone without visiting all edges. The algorithm has been applied to backbone identification in networks produced by random deposition of conductive sticks onto an insulating substrate. We have found that (i) for concentrations of sticks above the percolation threshold, the strength of the percolating cluster quickly approaches unity; (ii) simultaneously, the percolation cluster is identical to its backbone plus simplest dead ends, i.e., edges that are incident to vertices of unit degree.

Low temperature scanning tunneling spectroscopy of HfNiSn shows a V^m(m < 1) zero bias anomaly around the Fermi level. This local density of states with a fractional power law shape is well known to be a consequence of electronic correlations. For comparison, we have also measured the tunneling conductances of other half-Heusler compounds with 18 valence electrons. ZrNiPb shows a metal-like local density of states, whereas ZrCoSb and NbFeSb show a linear and V^2 anomaly. One interpretation of these anomalies is that a correlation gap is opening in these compounds. By analyzing the magnetoresistance of HfNiSn, we demonstrate that at low temperatures, electron-electron scattering dominates. The T^m(m < 1) temperature dependence of the conductivity confirms that the electronic correlations are a bulk rather than a surface property.

We construct a dynamical field theory for noninteracting Brownian particles in the presence of a quenched Gaussian random potential. The main variable for the field theory is the density fluctuation which measures the difference between the local density and its average value. The average density is spatially inhomogeneous for given realization of the random potential. It becomes uniform only after averaged over the disorder configurations. We develop the diagrammatic perturbation theory for the density correlation function and calculate the zero-frequency component of the response function exactly by summing all the diagrams contributing to it. From this exact result and the fluctuation dissipation relation, which holds in an equilibrium dynamics, we find that the connected density correlation function always decays to zero in the long-time limit for all values of disorder strength implying that the system always remains ergodic. This nonperturbative calculation relies on the simple diagrammatic structure of the present field theoretical scheme. We compare in detail our diagrammatic perturbation theory with the one used in a recent paper [B.\ Kim, M.\ Fuchs and V.\ Krakoviack, J.\ Stat.\ Mech.\ (2020) 023301], which uses the density fluctuation around the uniform average, and discuss the difference in the diagrammatic structures of the two formulations.

Systems with continuous symmetry of the vector order parameter containing defects of the "random local field" or "random local anisotropy" types are investigated. It is shown that the disordered Imry-Ma phase, in which the order parameter follows the spatial fluctuations of the random field or random anisotropy direction, can also occur in a coordinate space of dimension d higher than the lower critical dimension dl = 4. For this, the hyperplanes of dimension m < dl, must exist in the coordinate space in which there is a strong exchange interaction between spins, and the interaction between spins belonging to adjacent hyperplanes should not exceed a certain critical value.

We investigate the possibility of a many-body mobility edge in the Generalized Aubry-André (GAA) model with interactions using the Shift-Invert Matrix Product States (SIMPS) algorithm (Phys. Rev. Lett. 118, 017201 (2017)). The non-interacting GAA model is a one-dimensional quasiperiodic model with a self-duality induced mobility edge. The advantage of SIMPS is that it targets many-body states in an energy-resolved fashion and does not require all many-body states to be localized for convergence, which allows us to test if the interacting GAA model manifests a many-body mobility edge. Our analysis indicates that the targeted states in the presence of the single particle mobility edge match neither `MBL-like' fully-converged localized states nor the fully delocalized case where SIMPS fails to converge. An entanglement-scaling analysis as a function of the finite bond dimension indicates that the many-body states in the vicinity of a single-particle mobility edge behave closer to how delocalized states manifest within the SIMPS method.

In this study, we extend the lower bound on the average of the local energy of the Ising model with quenched randomness [J. Phys. Soc. Jpn. 76, 074711 (2007)] obtained for a symmetric distribution to an asymmetric one. Compared with the case of symmetric distribution, our bound has a non-trivial term. By applying the acquired bound to a Gaussian distribution, we obtain the lower bounds on the expectation of the square of the correlation function. Thus, we demonstrate that in the Ising model in a Gaussian random field, the spin-glass order parameter generally has a finite value at any temperature, regardless of the forms of the other interactions.

Tilings based on the cut and project method are key model systems for the description of aperiodic solids. Typically, quantities of interest in crystallography involve averaging over large patches, and are well defined only in the infinite-volume limit. In particular, this is the case for autocorrelation and diffraction measures. For cut and project systems, the averaging can conveniently be transferred to internal space, which means dealing with the corresponding windows. We illustrate this by the example of averaged shelling numbers for the Fibonacci tiling and review the standard approach to the diffraction for this example. Further, we discuss recent developments for inflation-symmetric cut and project structures, which are based on an internal counterpart of the renormalisation cocycle. Finally, we briefly review the notion of hyperuniformity, which has recently gained popularity, and its application to aperiodic structures.