Related papers: Phase diagram for hard-core $\mathbb{Z}_3$ anyons …
Anyons occur in two-dimensional electron systems as excitations with fractional charge in the topologically ordered states of the Fractional Quantum Hall Effect (FQHE). Their dynamics are of utmost importance for topological quantum phases…
An anyon exclusion statistics, which generalizes the Bose-Einstein and Fermi-Dirac statistics of bosons and fermions, was proposed by Haldane[1]. The relevant past studies had considered only anyon systems without any physical boundary but…
We analyze social and economic systems with a hierarchical structure and show that for such systems, it is possible to construct thermostatistics, based on the intermediate Gentile statistics. We show that in social and economic…
We introduce a novel class of low-dimensional topological tight-binding models that allow for bound states that are fractionally charged fermions and exhibit non-Abelian braiding statistics. The proposed model consists of a double (single)…
We present a comprehensive theoretical study of the phase diagram of a system of many Bose particles interacting with a two-body central potential of the so-called Lennard-Jones form. First-principles path-integral computations are carried…
We study a strongly interacting chain of anyons with fusion rules determined by SO(5)2. The phase portrait is identified with a combination of numerical and analytical techniques. Several critical phases with different central charges and…
Phase transitions are investigated in the Bose-Fermi-Hubbard model in the mean field and hard-core boson approximations for the case of infinitely small fermion transfer and repulsive on-site boson-fermion interaction. The behavior of the…
Recent cold atom experiments have realized one-dimensional anyons and enabled the tuning of 1D~statistics between bosons and fermions. Here, we analyze the symmetries, integrability, and resulting degeneracies of the underlying…
We consider particles in three-dimensional space, which have a certain probability to find themselves in a thin layer (``plane''), where they are assumed to be well described by a planar Hamiltonian and are subject to Aharonov-Bohm-type…
We discuss how to construct models of interacting anyons by generalizing quantum spin Hamiltonians to anyonic degrees of freedom. The simplest interactions energetically favor pairs of anyons to fuse into the trivial ("identity") channel,…
The fractional quantum Hall effect is a paradigm of topological order and has been studied thoroughly in two dimensions. Here, we construct a new type of fractional quantum Hall system, which has the special property that it lives in…
Low-energy excitations in spin 1/2 antiferromagnetic Heisenberg spin ladders are studied by bosonization and gauge theoretical description. It is explicitly shown that zero modes in the bosonization play an essentially important role.…
We demonstrate the emergence of non-Abelian fusion rules for excitations of a two dimensional lattice model built out of Abelian degrees of freedom. It can be considered as an extension of the usual toric code model on a two dimensional…
Anyons are exotic quasi-particles with fractional charge that can emerge as fundamental excitations of strongly interacting topological quantum phases of matter. Unlike ordinary fermions and bosons, they may obey non-abelian statistics--a…
The statistical distribution function of anyon is used to find the eighth viral coefficient in the high-temperature limit and the equation of state in the low-temperature limit. The perturbative results indicate that the thermodynamic…
This dissertation reports our investigation into the existence of anyons, which interpolate between bosons and fermions, in light of the Symmetrization Postulate, which states that only the two extremes exist. The Symmetrization Postulate…
The recent realization of mixed-dimensional systems of cold atoms has attracted much attention from both experimentalists and theorists. Different effective interactions and novel correlated quantum many-body phases may be engineered in…
Parafermions modes are non-Abelian anyons which were introduced as $\mathbb{Z}_N$ generalizations of $\mathbb{Z}_2$ Majorana states. In particular, $\mathbb{Z}_3$ parafermions can be used to produce Fibonacci anyons, laying a path towards…
We study a one-dimensional multicomponent anyon model that reduces to a multicomponent Lieb-Liniger gas of impenetrable bosons (Tonks-Girardeau gas) for vanishing statistics parameter. At fixed component densities, the coordinate Bethe…
A great part of the mathematical foundations of topological quantum computation is given by the theory of modular categories which provides a description of the topological phases of matter such as anyon systems. In the near future the…