Related papers: Simulation of braiding anyons using Matrix Product…
It is known that exact traveling wave solutions exist for families of (n+1)-states stochastic one-dimensional non-equilibrium lattice models with open boundaries provided that some constraints on the reaction rates are fulfilled. These…
We investigate a promising conformal field theory realization scheme for topological quantum computation based on the Fibonacci anyons, which are believed to be realized as quasiparticle excitations in the $\mathbb{Z}_3$ parafermion…
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…
Anyon colliders -- quantum Hall devices where dilute quasiparticle beams collide at a quantum point contact -- provide an interferometer-free probe of anyonic exchange phases through current cross correlations. Within a non-equilibrium…
We study two-component atomic gas mixtures in one dimension involving both bosons and fermions. When the inter-species interaction is attractive, we report a rich variety of coherent ground-state phases that vary with the intrinsic and…
Given a microscopic lattice Hamiltonian for a topologically ordered phase, we describe a tensor network approach to characterize its emergent anyon model and, in a chiral phase, also its gapless edge theory. First, a tensor network…
The microscopic control available over cold atoms in optical lattices has opened new opportunities to study the properties of quantum spin models. While a lot of attention is focussed on experimentally realizing ground or thermal states via…
Unlike bosons and fermions, quasi-particles in two-dimensional quantum systems, known as anyons, exhibit statistical exchange phases that range between $0$ and $\pi$. In fractional quantum Hall states, these anyons, possessing a fraction of…
Nontrivial topology in physical systems is the driving force behind many phenomena. Notably, phases of matter must be classified in part by their topological properties. Phases with topological order (TO), such as the fractional quantum…
Chiral symmetry is broken by typical interactions in lattice models, but the statistical interactions embodied in the anyon-Hubbard model are an exception. This is an example for a correlated hopping model where chiral symmetry protects a…
We provide a comprehensive systematic method for the numerical computation of elementary braid operations in topological quantum computation (TQC). This {procedure} is systematically applicable to all anyon models, including $SU(2)_k$.…
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…
Non-relativistic anyons in 1D possess generalized exchange statistics in which the exchange of two identical anyons generates a non-local phase that is governed by the spatial ordering of the particles and the statistical parameter…
We study a 2+1 dimensional theory of bosons and fermions with an omega ~ k^2 dispersion relation. The most general interactions consistent with specific symmetries impart fractional statistics to the fermions. Unlike examples involving…
We study the emergence of topological matter in two-dimensional systems of neutral Rydberg atoms in Ruby lattices. While Abelian anyons have been predicted in such systems, non-Abelian anyons, which would form a substrate for fault-tolerant…
Collective states of interacting non-Abelian anyons have recently been studied mostly in the context of certain fractional quantum Hall states, such as the Moore-Read state proposed to describe the physics of the quantum Hall plateau at…
Applying braided Yang-Baxter equation quantum integrable and Bethe ansatz solvable 1D anyonic lattice and field models are constructed. Along with known models we discover novel lattice anyonic and $q$-anyonic models as well as nonlinear…
Non-Abelian anyons, a promising platform for fault-tolerant topological quantum computation, adhere to the charge super-selection rule (cSSR), which imposes restrictions on physically allowed states and operations. However, the…
The discovery of fractional quantum anomalous Hall states in moir\'e systems has raised the interesting possibility of realizing phases of itenerant anyons. Anyon dispersion is only possible in the absence of continuous magnetic translation…
We propose and analyze the effect of anyonic interferometers that are designed such that the probe anyons traveling in a given path through the interferometer twist or braid around each other. These "twisted" interferometers are found to…