Related papers: Topology, phase transitions and the spherical mode…
Complex network theory has recently been proposed as a promising tool for characterising interactions between aircraft, and their downstream effects. We here explore the problem of networks' topological predictability, i.e. the dependence…
We explore the topology of configuration spaces of hard disks experimentally, and show that several changes in the topology can already be observed with a small number of particles. The results illustrate a theorem of Baryshnikov, Bubenik,…
The topology of a topological material can be encoded in its surface states. These surface states can only be removed by a bulk topological quantum phase transition into a trivial phase. Here we use photoemission spectroscopy to image the…
The present paper gives an account and quantifies the change in topology induced by small and type II geometric transitions, by introducing the notion of the \emph{homological type} of a geometric transition. The obtained results agree…
Geometrical approach to the phenomenological theory of phase transitions of the second kind at constant pressure $P$ and variable temperature $T$ is proposed. Equilibrium states of a system at zero external field and fixed $P$ and $T$ are…
We propose a novel network measure of topological invariants, called small-worldness, for identifying topological phase transitions of quantum and classical spin models. Small-worldness is usually defined in the study of social networks…
Topology is a powerful tool for categorizing magnetization textures by defining a topological index in both two-dimensional (2D) systems, such as thin films or curved surfaces, and in 3D bulk systems. In the emerging field of 3D…
The influence of topological defects on phase synchronization and phase coherence in two-dimensional arrays of locally-coupled, nonidentical, chaotic oscillators is investigated. The motion of topological defects leads to a breakdown of…
A topological approach to the theory of equilibrium phase transitions in statistical physics is based on the Topological Hypothesis (TH), which claims that phase transitions are due to changes of the topology of suitable submanifolds in the…
The central goal of this thesis is to develop methods to experimentally study topological phases. We do so by applying the powerful toolbox of quantum simulation techniques with cold atoms in optical lattices. To this day, a complete…
We consider the phase transition in a model which consists of a Ginzburg-Landau free energy for superconductors including a Chern-Simons term. The mean field theory of Halperin, Lubensky and Ma [Phys. Rev. Lett. 32, 292 (1974)] is applied…
Topological phase transitions challenge conventional paradigms in many-body physics by separating phases that are locally indistinguishable yet globally distinct. Using a quantum simulator of interacting erbium atoms in an optical lattice,…
By stacking PbTe layers there is a non-monotonic topological phase transition as a function of the number of monolayers. Based on first principles calculations we find that the proper stacked crystal symmetry determines the topological…
We present a general recipe to describe topological phase transitions in condensed matter systems with interactions. We show that topological invariants in the presence of interactions can be efficiently calculated by means of a…
We demonstrate the existence of a new topologically ordered phase in Kitaev's honeycomb lattice model. This new phase appears due to the presence of a vortex lattice and it supports chiral Abelian anyons. We characterize the phase by its…
Persistent homology analysis, a recently developed computational method in algebraic topology, is applied to the study of the phase transitions undergone by the so-called XY-mean field model and by the phi^4 lattice model, respectively. For…
A characteristic feature of topological systems is the presence of robust gapless edge states. In this work the effect of time-dependent perturbations on the edge states is considered. Specifically we consider perturbations that can be…
Topological phase transitions can be described by the theory of critical phenomena and identified by critical exponents that define their universality classes. This is a consequence of the existence of a diverging length at the transition…
We demonstrate the identification and classification of topological phase transitions from experimental data using Diffusion Maps: a nonlocal unsupervised machine learning method. We analyze experimental data from an optical system…
The recently discovered three dimensional or bulk topological insulators are expected to exhibit exotic quantum phenomena. It is believed that a trivial insulator can be twisted into a topological state by modulating the spin-orbit…