Related papers: Boson-Lattice Construction for Anyon Models
Anyon models are algebraic structures that model universal topological properties in topological phases of matter and can be regarded as mathematical characterization of topological order in two spacial dimensions. It is conjectured that…
We propose a simple scheme for realizing the physics of 1D anyons with ultracold bosonic atoms in an optical lattice. It relies on lattice-shaking-induced resonant tunneling against potential off-sets created by a combination of a lattice…
A local quantum bosonic model on a lattice is constructed whose low energy excitations are gravitons described by linearized Einstein action. Thus the bosonic model is a quantum theory of gravity, at least at the linear level. We find that…
We establish an exact mapping between identical particles in one dimension with arbitrary exchange statistics, including bosons, anyons and fermions, provided they share the same scattering length. This boson-anyon-fermion mapping…
It has been demonstrated numerically, mainly by considering ground state properties, that fractional quantum Hall physics can appear in lattice systems, but it is very difficult to study the anyons directly. Here, I propose to solve this…
Anyons are particlelike excitations of strongly correlated phases of matter with fractional statistics, characterized by nontrivial changes in the wave function, generalizing Bose and Fermi statistics, when two of them are interchanged.…
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…
We introduce a construction of symmetry-enriched topological orders on bipartite lattices in which two $\mathbb{Z}_2$ spin liquids defined on each sublattice are combined, and then anyons are condensed to reduce the topological order. By…
We reconsider the problem of anyons on higher genus surfaces by embedding them in three dimensional space. From a concrete realization based on three dimensional flux tubes bound to charges moving on the surface, we explicitly derive all…
We proposed an entangled multi-knot lattice model to explore the exotic statistics of anyon. This knot lattice model bears abelian and non-abelian anyons as well as integral and fractional filling states that is similar to quantum Hall…
Anyon models can be symmetric under some permutations of their topological charges. One can then conceive topological defects that, under monodromy, transform anyons according to a symmetry. We study the realization of such defects in the…
Generating physically buildable brick structures from 3D shapes requires more than geometric reconstruction: the output must also satisfy discrete part constraints and structural stability. Existing brick generation methods either rely on…
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…
Anyons obeying fractional exchange statistics arise naturally in two dimensions: hard-core two-body constraints make the configuration space of particles not simply-connected. The braid group describes how topologically-inequivalent…
We try to increase the fundamental symmetries of the anyonic particle with the help of the symplectic formalism of constrained systems and gauging the model. The main idea of this approach is based on the embedding of the model in an…
We construct (2+1)-dimensional lattice systems, which we call fusion surface models. These models have finite non-invertible symmetries described by general fusion 2-categories. Our method can be applied to build microscopic models with,…
q-bosonic realization of the underlying Yang-Baxter algebra is identified for a series of quantum integrable systems, including some new models like two-mode q-bosonic model leading to a coupled two-component derivative NLS model, wide…
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 show that the "geometric models of matter" approach proposed by the first author can be used to construct models of anyon quasiparticles with fractional quantum numbers, using 4-dimensional edge-cone orbifold geometries with orbifold…
A generic method for combinatorial constructions of intrinsic geometrical spaces is presented. It is based on the well known inverse sequences of finite graphs that determine (in the limit) topological spaces. If a pattern of the…