Related papers: Microscopic definitions of anyon data
To the working physicist, anyon theory is meant to describe certain quasi-particle excitations occurring in two dimensional topologically ordered systems. A typical calculation using this theory will involve operations such as $\otimes$ to…
We introduce a pentagon equation solver, available as part of SageMath, and use it to construct braid group representations associated to certain anyon systems. We recall the category-theoretic framework for topological quantum computation…
Anyons are quasiparticles in two-dimensional systems that show statistical properties very distinct from those of bosons or fermions. While their isolated observation has not yet been achieved, here we perform a quantum simulation of anyons…
We investigate the enlarged class of open finite strings in $(2+1)D$ space-time. The new dynamical system related to this class is constructed and quantized here. As the result, the energy spectrum of the model is defined by a simple…
For fixed natural numbers $r$ and $s$, where $2\leq s \leq r$, we consider a representation of numbers from the interval $[0;\frac{r}{s-1}]$ obtained by encoding numbers by means of the alphabet $A=\{0,1,...,r\}$ via the expansion…
The possibility of excitations with fractional spin and statististics in $1+1$ dimensions is explored. The configuration space of a two-particle system is the half-line. This makes the Hamiltonian self-adjoint for a family of boundary…
The quantum-mechanical description of assemblies of particles whose motion is confined to two (or one) spatial dimensions offers many possibilities that are distinct from bosons and fermions. We call such particles anyons. The simplest…
Symbolic regression is the machine learning method for learning functions from data. After a brief overview of the symbolic regression landscape, I will describe the two main challenges that traditional algorithms face: they have an unknown…
The question of anyons and fractional statistics in field theories in 2+1 dimensions with Chern-Simons (CS) term is discussed in some detail. Arguments are spelled out as to why fractional statistics is only possible in two space…
The string-net model describes a vast family of topological orders in two spatial dimensions. Here, we consider the effect of thermal fluctuations on these topological phases. In the original string-net model, the description of charge…
We introduce and describe in second quantization a family of particle species with \(p=2,3,\dots\) exclusion and \(\theta=2\pi/p\) exchange statistics. We call these anyons Fock parafermions, because they are the particles naturally…
In spacetime dimensions of 4 (i.e., 3+1) and higher, topological orders exhibit spatially extended excitations like loops and membranes, which support diverse topological data characterizing braiding, fusion, and shrinking processes,…
In some real world situations, linear models are not sufficient to represent accurately complex relations between input variables and output variables of a studied system. Multilayer Perceptrons are one of the most successful non-linear…
The operational formalism to quantum mechanics seeks to base the theory on a firm foundation of physically well-motivated axioms [1]. It has succeeded in deriving the Feynman rules [2] for general quantum systems. Additional elaborations…
Functional decomposition is the process of breaking down a function $f$ into a composition $f=g(f_1,\dots,f_k)$ of simpler functions $f_1,\dots,f_k$ belonging to some class $\mathcal{F}$. This fundamental notion can be used to model…
In our recent paper (Phys. Rev. B 76, 075403 (2007)), we have applied the anyon concept to derive an approximate analytic formula for the ground state energy, which applies to two-dimensional (2D) Coulomb systems from the bosonic to the…
An overview is given of the 2D many-anyon gas, including its definition (both for ideal and certain less-than-ideal particles, as well as for abelian and nonabelian braid group representations), its corresponding known properties starting…
We show that the anyonic statistics of fractionalized excitations display characteristic signatures in threshold spectroscopic measurements. Drawing motivation from topologically ordered phases such as gapped quantum spin liquids and…
Table extraction is an important but still unsolved problem. In this paper, we introduce a flexible and modular table extraction system. We develop two rule-based algorithms that perform the complete table recognition process, including…
Understanding a neural code requires knowledge both of the elementary symbols that transmit information and of the algorithm for translating these symbols into sensory signals or motor actions. We show that these questions can be separated:…