Thirty years ago, scientists first observed that when a small amount of gold is deposited on the surface of silicon, both the gold and silicon atoms automatically organize themselves into parallel linear rows, so-called "atom chains", with nearly perfect structural order. This observation marked the beginning of a new research direction in which theoretical predictions about "physics in one dimension" could now be investigated experimentally using the standard tools of surface science such as scanning tunneling microscopy, x-ray diffraction, and photoemission. A particularly striking discovery, first reported ten years ago, was that at low temperature the silicon chains can develop local magnetic moments, which form regular highly ordered, periodic patterns. These "silicon spin chains" have now become the main focus of this research field. This talk will describe three recent theoretical and experimental aspects of silicon spin chains: the possibility of magnetic ordering in these one-dimensional systems; the prospects for using surface chemistry to tailor spin chains by creating or destroying individual spins; and the properties and dynamics of solitons in the spin chains.
The edge count in the neighbourhood of a node in a complex network of interactions, after rescaling by the number of possible edges, gives the local clustering coefficient. This is averaged over all nodes in the network to give the global clustering coefficient. Interestingly, topological spaces built on neighbourhoods can display diverse homology which does not effect this edge count, suggesting we should investigate the neighbourhood’s homology scaling with respect to its clustering. We show how the number of connected componets, cycles, voids, and ultimately the Euler characteristic of the clique complex built on the neighbourhood are related to clustering in some web, social and transportation networks, specifically by contrasting with the random clique and Vietoris-Rips complex. This applies some recent results from the expected topology of random simplicial complexes. We find power laws for the scaling of the zeroth Betti number (number of connected components) with the local clustering coefficient, a unimodal rising and falling behaviour of the first Betti number (number of 1d holes), and evidence of universal homology scaling throughout the random models and dataset categories. These random models, however, do not replicate the `order independence' of the homology scaling with clustering observed in almost all the datasets, which is a new characteristic of hierarchical community structure not present in random complexes, or random geometric complexes. In particular, the random models show the number of k-dimensional holes changing exponentially with clustering in the hubs, but as a power law in the periphery. The data sets, however, show power law decay of the number of holes throughout the periphery, bridge, and hubs, as hinted at by early work of Ravasz and Barabasi in 2003, who study only the clustering with respect to the neighbourhood size.
A fundamental assumption in statistical physics is that generic closed quantum many-body systems thermalise under their own dynamics. Recently, the emergence of many-body localised (MBL) systems has questioned this concept, challenging our understanding of the connection between statistical physics and quantum mechanics. In my talk, I will report on several recent experiments carried out in our group on the observation of Many-Body Localisation in different scenarios, ranging from 1D fermionic quantum gas mixtures in driven and undriven Aubry-André type disorder potentials and 2D systems of interacting bosons in 2D random potentials. It is shown that the memory of the system on its initial non-equilibrium state can serve as a useful indicator for a non-ergodic, MBL phase. Furthermore, I will present new results on the slow relaxation dynamics in the ergodic phase below the MBL transition and experiments that explore the resilience of a 2D MBL phase when coupled to a finite thermal bath. Our experiments represent a demonstration and in-depth characterisation of many-body localisation, often in regimes not accessible with state-of-the-art simulations on classical computers.