Related papers: Shadows of Anyons
In this first paper, we demonstrate a theorem that establishes a first step toward proving a necessary topological condition for the occurrence of first or second order phase transitions: we prove that the topology of certain submanifolds…
The content of this thesis can be broadly summarised into two categories: first, I constructed modified numerical algorithms based on tensor networks to simulate systems of anyons in low dimensions, and second, I used those methods to study…
Novel classical wave phenomenon analogs of the quantum spin Hall effect are mostly based on the construction of pseudo-spins. Here we show that the non-trivial topology of a system can also be realized using orbital angular momentum through…
Entanglement is a special feature of the quantum world that reflects the existence of subtle, often non-local, correlations between local degrees of freedom. In topological theories such non-local correlations can be given a very intuitive…
The standard Landau-Ginzburg scenario of phase transition is broken down for quantum phase transition. It is difficult to find an order parameter to indicate different phases for quantum fluctuations. Here, we suggest a topological…
In this thesis we develop a full characterization of abelian quantum statistics on graphs. We explain how the number of anyon phases is related to connectivity. For 2-connected graphs the independence of quantum statistics with respect to…
In recent years, the import of quantum information techniques in quantum gravity opened new perspectives in the study of the microscopic structure of spacetime. We contribute to such a program by establishing a precise correspondence…
We show that quantum systems of extended objects naturally give rise to a large class of exotic phases - namely topological phases. These phases occur when the extended objects, called ``string-nets'', become highly fluctuating and…
In this paper, we explore topological quantum computation augmented by subphases and phase transitions. We commence by investigating the anyon tunneling map, denoted as $\varphi$, between subphases of the quantum double model…
Studying quantum entanglement in systems of indistinguishable particles, in particular anyons, poses subtle challenges. Here, we investigate a model of one-dimensional anyons defined by a generalized algebra. This algebra has the special…
Tensor networks provide a powerful new framework for classifying and simulating correlated and topological phases of quantum matter. Their central premise is that strongly correlated matter can only be understood by studying the underlying…
The theory of quantum computation can be constructed from the abstract study of anyonic systems. In mathematical terms, these are unitary topological modular functors. They underlie the Jones polynomial and arise in Witten-Chern-Simons…
Quantum networks offer a realistic and practical scheme for generating multiparticle entanglement and implementing multiparticle quantum communication protocols. However, the correlations that can be generated in networks with quantum…
We study the stability of topological order against local perturbations by considering the effect of a magnetic field on a spin model -- the toric code -- which is in a topological phase. The model can be mapped onto a quantum loop gas…
Quantum contextuality, a fundamental feature distinguishing quantum theory from classical models, is investigated via algebraic and topological structures inherent in modular tensor categories. This work rigorously demonstrates that braid…
These extended lecture notes survey a novel derivation of anyonic topological order (as seen in fractional quantum Hall systems) on single magnetized M5-branes probing Seifert orbi-singularities ("geometric engineering" of anyons), which we…
We present a unified category-theoretic framework for quantum Hall hierarchy constructions and anyon superconductivity based on modular tensor categories over $\mathrm{Rep}(\mathrm{U}(1))$ and $\mathrm{sRep}(\mathrm{U}(1)^f)$. Our approach…
Topology plays a cardinal role in explaining phases and quantum phase transitions beyond the Landau-Ginzburg-Wilson paradigm. In this study, we formulate a set of models of Dirac fermions in 2+1 dimensions with…
Tensor network states, and in particular projected entangled pair states, play an important role in the description of strongly correlated quantum lattice systems. They do not only serve as variational states in numerical simulation…
The transition from the quantum to the classical regime of the nucleation of the closed Robertson-Walker Universe with spacially homogeneous matter fields is investigated with a perturbation expansion around the sphaleron configuration. A…