Adiabatic Heuristic Principle on a Torus and Generalized Streda Formula

Adiabatic Continuity of the Spinful Quantum Hall States

By using the extended Hubbard model of anyons, we numerically demonstrate the adiabatic deformation of the spinful quantum Hall (QH) states by transmutation of statistical fluxes. While the ground state is always spin-polarized in a series of $ν=1$ integer QH system, the adiabatic continuity between the singlet QH states at $ν=2$ and $ν=2/5$ is confirmed. These results are consistent with the composite fermion theory with spin. The many-body Chern number of the ground state multiplet works as an adiabatic invariant and also explains the wild change of the topological degeneracy during the evol…

从有效薄环面极限绝热制备分数陈绝缘体

Adiabatic preparation of fractional Chern insulators from an effective thin-torus limit

本研究提出以分数陈绝缘体的准一维薄环面极限为起点，通过调控单方向跃迁幅度改变系统有效纵横比，构建连接电荷密度波基态与分数陈绝缘体态的绝热路径，结合解析计算与精确对角化数值模拟验证了该方案用于大尺寸分数陈绝缘体制备的可行性。

Bulk-edge Correspondence in the Adiabatic Heuristic Principle

Using the Laughlin's argument on a torus with two pin-holes, we numerically demonstrate that the discontinuities of the center-of-mass work well as an invariant of the pumping phenomena during the process of the flux-attachment, trading the magnetic flux for the statistical one. This is consistent with the bulk-edge correspondence of the fractional quantum Hall effect of anyons. We also confirm that the general feature of the edge states remains unchanged during the process while the topological degeneracy is discretely changed. This supports the stability of the quantum Hall edge states in th…

Composite anyons on a torus

An adiabatic approach put forward by Greiter and Wilczek interpolates between the integer quantum Hall effects of electrons and composite fermions by varying the statistical flux bound to electrons continuously from zero to an even integer number of flux quanta, such that the intermediate states represent anyons in an external magnetic field with the same "effective" integer filling factor. We consider such anyons on a torus, and construct representative wave functions for their ground as well as excited states. These wave functions involve higher Landau levels in general, but can be explicitl…

Abelian and non-Abelian statistics in the coherent state representation

We further develop an approach to identify the braiding statistics associated to a given fractional quantum Hall state through adiabatic transport of quasiparticles. This approach is based on the notion of adiabatic continuity between quantum Hall states on the torus and simple product states---or "patterns"---in the thin torus limit, together with a suitable coherent state Ansatz for localized quasiholes that respects the modular invariance of the torus. We give a refined and unified account of the application of this method to the Laughlin and Moore-Read states, which may serve as a pedagogi…