Related papers: General procedure for determining braiding and sta…
Topologically ordered phases are gapped states, defined by the properties of excitations when taken around one another. Here we demonstrate a method to extract the statistics and braiding of excitations, given just the set of ground-state…
A topological order is a new quantum phase that is beyond Landau's symmetry-breaking paradigm. Its defining features include robust degenerate ground states, long-range entanglement and anyons. It was known that $R$- and $F$-matrices, which…
Indistinguishability of particles is a fundamental principle of quantum mechanics. For all elementary and quasiparticles observed to date - including fermions, bosons, and Abelian anyons - this principle guarantees that the braiding of…
Topological quantum computation employs two-dimensional quasiparticles called anyons. The generally accepted mathematical basis for the theory of anyons is the framework of modular tensor categories. That framework involves a substantial…
We demonstrate that the anyon statistics and three-loop statistics of various 2d and 3d topological phases can be derived using semiclassical nonlinear Sigma model field theories with a topological $\Theta$-term. In our formalism, the…
Topological quantum states of matter, both Abelian and non-Abelian, are characterized by excitations whose wavefunctions undergo non-trivial statistical transformations as one excitation is moved (braided) around another. Topological…
It is well-known that many topological phase transitions of intrinsic Abelian topological phases are accompanied by condensation and confinement of anyons. However, for non-Abelian topological phases, more intricate phenomena can occur at…
Even-denominator quantum Hall states can host several types of anyons with distinct exchange statistics. Depending on the anyon type, exchanging two quasiparticles can impart a phase to the many-body wave function or even transform it into…
The classification and characterization of topological phases of matter is well understood for ground states of gapped Hamiltonians that are well isolated from the environment. However, decoherence due to interactions with the environment…
Anyons are quasiparticles with fractional statistics, bridging between fermions and bosons. We propose an experimental setup to measure the statistical angle of topological anyons emitted from a quantum point contact (QPC) source. The setup…
Coherent control and braiding of anyons remain central challenges in realizing topologically protected quantum operations. We propose a Ramsey interferometry protocol to directly access the geometric phases associated with anyons in…
We study various aspects of the topological quantum computation scheme based on the non-Abelian anyons corresponding to fractional quantum hall effect states at filling fraction 5/2 using the Temperley-Lieb recoupling theory. Unitary…
Here we show how the Minimally Entangled States (MES) of a 2d system with topological order can be identified using the geometric measure of entanglement. We show this by minimizing this measure for the doubled semion, doubled Fibonacci and…
The role of anyonic statistics stands as a cornerstone in the landscape of topological quantum techniques. While recent years have brought forth encouraging and persuasive strides in detecting anyons, a significant facet remains unexplored,…
We comment on the significance of the results in the paper by Nakamura et al (2020). The experimental result measures the phase for a repeated elementary exchange of two identical quasiparticles, and shows that the quasiparticles are…
The search for anyons, quasiparticles with fractional charge and exotic exchange statistics, has inspired decades of condensed matter research. Quantum Hall interferometers enable direct observation of the anyon braiding phase via discrete…
Correlations of partitioned particles carry essential information about their quantumness. Partitioning full beams of charged particles leads to current fluctuations, with their autocorrelation (namely, shot noise) revealing the particle'…
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…
Anyons exist as point like particles in two dimensions and carry braid statistics which enable interactions that are independent of the distance between the particles. Except for a relatively few number of models which are analytically…
We demonstrate that anyons on wire networks have fundamentally different braiding properties than anyons in 2D. Our analysis reveals an unexpectedly wide variety of possible non-abelian braiding behaviours on networks. The character of…