Entanglement spectrum of non-Abelian anyons

Non-Abelian anyons can emerge as fractionalized excitations in two-dimensional systems with topological order. One important example is the Moore–Read fractional quantum Hall state. Its quasihole states are zero-energy eigenstates of a parent Hamiltonian, but its quasiparticle states are not. Both of them can be modeled on an equal footing using the bipartite composite fermion method. We study the entanglement spectrum of the cases with two or four non-Abelian anyons. The counting of levels in the entanglement spectrum can be understood using the edge theory of the Moore–Read state, which reflects the topological order of the system. It is shown that the fusion results of two non-Abelian anyons is determined by their distributions in the bipartite construction.

Simulation of anyons by cold atoms with induced electric dipole moment

We show that it is possible to simulate an anyon by a trapped atom which possesses an induced electric dipole moment in the background of electric and magnetic fields in a specific configuration.The electric and magnetic fields we applied contain a magnetic and two electric fields.We find that when the atom is cooled down to the limit of the negligibly small kinetic energy,the atom behaves like an anyon because its angular momentum takes fractional values.The fractional part of the angular momentum is determined by both the magnetic and one of the electric fields.Roles electric and magnetic fields played are analyzed.

Golden Anyons for Cosmic Dark Energy Density

The note gives a watertight confirmation of the E-infinity Cantorian theory results for ordinary and dark cosmic energy density of the universe and respectively. The computation is fundamentally based on a golden mean fusion function that goes back to the highly original anyon proposal of F. Wilczek.

A Scheme for Simulation of Quantum Gates by Abelian Anyons

Anyons can be used to realize quantum computation, because they are two-level systems in two dimensions. In this paper, we propose a scheme to simulate single-qubit gates and CNOT gate using Abelian anyons in the Kitaev model. Two pairs of anyons （six spins） are used to realize single-qubit gates, while ten spins are needed for the CNOT gate. Based on these quantum gates, we show how to realize the Grover algorithm in a two-qubit system.

Some Topological Properties of Anyons

In this paper,starting with the well known U(1)Chern-Simons Lagrangian and the covariant derivative ofa complex scalar matter field,we give a detailed discussion of some topological properties of anyons.We show that the'basic'charge carried by anyons has an inner structure and can be decomposed in terms of the Chern-Simons couplingand the gauge coupling constants of the theory.Also some incorrect results obtained in the literature are revised.

Recent progress on non-Abelian anyons:from Majorana zero modes to topological Dirac fermionic modes

Majorana zero modes(MZMs)have been intensively studied in recent decades theoretically and experimentally as the most promising candidate for non-Abelian anyons supporting topological quantum computation(TQC).In addition to the Majorana scheme,some non-Majorana quasiparticles obeying non-Abelian statistics,including topological Dirac fermionic modes,have also been proposed and therefore become new candidates for TQC.In this review,we overview the non-Abelian braiding properties as well as the corresponding braiding schemes for both the MZMs and the topological Dirac fermionic modes,emphasizing the recent progress on topological Dirac fermionic modes.A topological Dirac fermionic mode can be regarded as a pair of MZMs related by unitary symmetry,which can be realized in a number of platforms,including the one-dimensional topological insulator,higher-order topological insulator,and spin superconductor.This topological Dirac fermionic mode possesses several advantages compared with its Majorana cousin,such as superconductivity-free and larger gaps.Therefore,it provides a new avenue for investigating non-Abelian physics and possible TQC.

Wave equation for anyons and its exact solutions in external fields

<正> By using the gauge-invariance,a Klein-Gordon’s type equation for anyons in external fields is constructed.The equation can be solved exactly in a constant electric and magnetic field,as well as in a quantized electromagnetic field.The analytic forms of solutions are also given in detail.

在anyon模型中空穴的有效吸引作用

在Laughlin等人的anyon模型框架下,确证空穴间的有效吸引作用,并由此产生超导电性。

Rotational symmetry of classical orbits, arbitrary quantization of angular momentum and the role of the gauge field in two-dimensional space

We study quantum classical correspondence in terms of the coherent wave functions of a charged particle in two-dimensional central-scalar potentials as well as the gauge field of a magnetic flux in the sense that the probability clouds of wave functions are well localized on classical orbits. For both closed and open classical orbits, the non-integer angular-momentum quantization with the level space of angular momentum being greater or less than h is determined uniquely by the same rotational symmetry of classical orbits and probability clouds of coherent wave functions, which is not necessarily 27r-periodic. The gauge potential of a magnetic flux impenetrable to the particle cannot change the quantization rule but is able to shift the spectrum of canonical angular momentum by a flux-dependent value, which results in a common topological phase for all wave functions in the given model. The well-known quantum mechanical anyon model becomes a special case of the arbitrary quantization, where the classical orbits are 2π-periodic.

Entangled multi-knot lattice model of anyon current

We proposed an entangled multi-knot lattice model to explore the exotic statistics of anyons. Long-range coupling interaction is a fundamental character of this knot lattice model. The short-range coupling models, such as the Ising model,Hamiltonian model of quantum Hall effect, fermion pairing model, Kitaev honeycomb lattice model, and so on, are the short-range coupling cases of this knot lattice model. The long-range coupling knot lattice model bears Abelian and nonAbelian anyons, and shows integral and fractional filling states like the quantum Hall system. The fusion rules of anyons are explicitly demonstrated by braiding crossing states. The eigenstates of quantum models can be represented by a multilayer link lattice pattern whose topology is characterized by the linking number. This topological linking number offers a new quantity to explain and predict physical phenomena in conventional quantum models. For example, a convection flow loop is introduced into the well-known Bardeen–Cooper–Schrieffer fermion pairing model to form a vortex dimer state that offers an explanation of the pseudogap state of unconventional superconductors, and predicts a fractionally filled vortex dimer state. The integrally and fractionally quantized Hall conductance in the conventional quantum Hall system has an exact correspondence with the linking number in this multi-knot lattice model. The real-space knot pattern in the topological insulator model has an equivalent correspondence with the Lissajous knot in momentum space. The quantum phase transition between different quantum states of the quantum spin model is also directly quantified by the change of topological linking number, which revealed the topological character of phase transition. Circularized photons in an optical fiber network are a promising physical implementation of this multi-knot lattice, and provide a different path to topological quantum computation.

谈谈基础阶段教学的几个问题(英文)

The way of teaching in the early stages has been the question of discussion for years. Here I will limit myself to five points: (1) to help the students form good habits of learning; (2) to teach the students the perfection of the English sound system; (3) to help the students form good habits of reading; (4) to teach grammar in speech, not by constructing sentences according to rules; (5) to reduce to a minimum the use of translation by the learning of vocabulary. My aim is to put the question for further discussion.

Limiting Case of 1D Delta Anyon Model

In order to analyze a limiting case of the 1D delta anyon model,the coupling strength of the δ interactionc is modified to become a function of the anyonic parameter κ.A pedagogic derivation of the solution for this modifiedmodel using the method of anyon-boson mapping plus Bethe ansatz is presented.The limiting case as κ→π andsimultaneously c→0,which was previously neglected,is analyzed.Some unexpected properties of this limiting case arediscovered.The BAEs are compared with previous results.

An Anyon Model in a Toric Honeycomb Lattice

We study an anyon model in a toric honeycomb lattice. The ground states and the low-lying excitations coincide with those of Kitaev toric code model and then the excitations obey mutual semionic statistics. This model is helpful to understand the toric code of anyons in a more symmetric way. On the other hand, there is a direct relation between this toric honeycomb model and a boundary coupled Ising chain array in a square lattice via Jordan-Wigner transformation. We discuss the equivalence between these two models in the low-lying sector and realize these anyon excitations in a conventional fermion system. The analysis for the ground state degeneracy in the last section can also be thought of as a complementarity of our previous work [Phys. A： Math. Theor. 43 （2010） 105306].

Marxism and Political Economy in Education:An Interpretation of Jean Anyon's Critical Pedagogy

Jean Anyon(1941-2013)is a critical pedagogical researcher and social activist in the United States.All her life,she devoted herself to taking education as a breakthrough,exposing the ugliness of capitalist countries and promoting the equality of society and education.She uses Marxist theory to analyze the relationship between social class and school knowledge,hidden curriculum;education and mainstream ideology;and conflicts and resistances in education,emphasizing the theoretical and practical significance of Marxism in today’s education.In order to find the deepest problem of education,Jean Anyon demonstrates the relationship between school education and macroeconomic policy from the perspective of political economics;the dialectical relationship between education reform and economic reform;and explains the reasons for education failure by quoting David Harvey’s concept of“deprivation accumulation”.Facing the cruel situation,Jean Anyon did not lose confidence,but found the“radical possibility”and put forward the concept of social change centered on education reform.

A Model for the Quantization of the Hall Resistance in the Quantum Hall Effect

Some aspects of anyon physics are reviewed with the intention of establishing a model for the quantization of the Hall conductance. A single particle Schr&#246;dinger model is introduced and coupled with a constraint equation formulated from the anyon picture. The Schr&#246;dinger equation-constraint system can be converted to a single nonlinear differential equation and solutions for the model can be produced.

我的天地

我在家里的房间很小,偏偏我平时又喜欢搜集一些可爱的小玩意,几年下来,各种各样小玩意就渐渐摆满了我的房间。对那些摆放不下的东西,我只好忍痛将他们打包放进纸箱里,然后再塞进家里大大小小的储物柜里面,通常情况下我都不记得这些东西的具体存放位置。

Rotational symmetry of classical orbits, arbitrary quantization of angular momentum and the role of the gauge field in two-dimensional space

We study quantum–classical correspondence in terms of the coherent wave functions of a charged particle in two- dimensional central-scalar potentials as well as the gauge field of a magnetic flux in the sense that the probability clouds of wave functions are well localized on classical orbits. For both closed and open classical orbits, the non-integer angular-momentum quantization with the level space of angular momentum being greater or less than is determined uniquely by the same rotational symmetry of classical orbits and probability clouds of coherent wave functions, which is not necessarily 2π-periodic. The gauge potential of a magnetic flux impenetrable to the particle cannot change the quantization rule but is able to shift the spectrum of canonical angular momentum by a flux-dependent value, which results in a common topological phase for all wave functions in the given model. The well-known quantum mechanical anyon model becomes a special case of the arbitrary quantization, where the classical orbits are 2π-periodic.