An elementary rigorous proof of bulk-boundary correspondence in the generalized Su-Schrieffer-Heeger model

We generalize the Su-Schrieffer-Heeger (SSH) model with the inclusion of arbitrary long-range hopping amplitudes, providing a simple framework to investigate arbitrary adiabatic deformations that preserve the chiral symmetry upon the bulk energy bands with any arbitrary winding numbers. Using only elementary techniques of solving linear difference equations and applying Cauchy's integral formula, we obtain a mathematically rigorous and physically transparent proof of the bulk-boundary correspondence for the generalized SSH model. The multiplicity of robust zero-energy edge modes is shown to be identical to the winding number. On the other hand, nonzero-energy edge modes, if any, are shown to be unstable under adiabatic deformations and not related to the topological invariant. Furthermore, under deformations of small spatial disorder, the zero-energy edge modes remain robust.     

Localized States of a Narrow Single-Walled Carbon Nanotube by Using Su-Schrieffer-Heeger Model Hamiltonian

As a continuation of our previous work [N. Sünel and O. Özsoy: Int. J. Quant. Chem., Vol. 99 (2004)] on deriving the most general matrix representations, we investigate localized states of a carbon sheet and those of a single-walled carbon nanotube and of a nanotorus within the extended Su-Schrieffer-Heeger model.     

规范场和夸克动力学模型——关于QCD和层子模型的议论

文章讨论了夸克QCD模型和层子模型的关系,说明夸克动力学模型的基础是非亚贝尔规范场理论.层子模型是半唯象理论,没有动力学互作用的机制.QCD由于以非亚贝尔规范场为动力学互作用机制,在高能行为有渐近自由的重要性质.层子模型是低能束缚态的唯象性质的模型,与渐近自由是完全无关.强调“渐近自由”是一个独立于夸克模型的物理概念,它的理论基础是非亚贝尔规范场理论;当把非亚贝尔规范场作为夸克相互作用建立了夸克的动力学模型——量子色动力学（quantum chromodynamics,QCD）;层子模型是想把静态夸克模型发展为动力学模型,但它走的路线与QCD完全不同,层子的互作用不涉及非亚贝尔规范场,与渐近自由是不同概念和不同思想和不同考察区域;文章还指出夸克动力学的QCD模型同层子模型是哲学思想不同,物理思想也不相同的路线,层子模型没有接纳非亚贝尔规范场而未能达成创新的成果.文章也强调三十多年前层子模型研究的创新意识和团队精神是我们值得推崇的优秀传统.     

Regular solutions in the Skyrme model with gauge field

A study is made of the Skyrme model with gauge field, which admits the existence of regular solutions with nontrivial topological charge. It is shown that the solution with unit charge realizes a minimum of the energy of the system and therefore corresponds to a stable particle. A qualitative analysis of the Euler-Lagrange equations is made, approximate solutions to them being found by a variational method for several values of the parameters of the model.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 13–17, September, 1980.     

扩展Su-Schrieffer-Heeger模型在周期性边界条件下的相变

文章计算了含有三种跃迁项(最近邻(NN)、次近邻(NNN)、次次近邻(NNNN)跃迁项)的扩展Su-Schrieffer-Heeger(SSH)模型(模型ⅰ)的热力学特性.对仅含有二种跃迁项(NN、NNN跃迁项)的扩展SSH模型(模型ⅱ)、仅含有一种跃迁项(NN跃迁项)的SSH模型(模型ⅲ)也作了类似的计算.在低温下,每个模型都有相变且跃迁项的存在会降低相变温度.由于NNN跃迁项的存在,在极低温条件下,关于热容量与温度比(HCOTR)随温度变化的单调性,模型i与其它两个模型存在差异.在低温下,模型ⅰ的HCOTR的单调性,会受NN或NNN或NNNN跃迁项的影响并且NN或NNN跃迁项会影响其相变.     

Topological states in the Hofstadter model on a honeycomb lattice

We provide a detailed analysis of a topological structure of a fermion spectrum in the Hofstadter model with different hopping integrals along the $x,y,z$-links ($t_x=t,t_y=t_z=1$), defined on a honeycomb lattice. We have shown that the chiral gapless edge modes are described in the framework of the generalized Kitaev chain formalism, which makes it possible to calculate the Hall conductance of subbands for different filling and an arbitrary magnetic flux ϕ. At half-filling the gap in the center of the fermion spectrum opens for $t>t_c=2^{\varphi }$, a quantum phase transition in the 2D-topological insulator state is realized at $t_c$. The phase state is characterized by zero energy Majorana states localized at the boundaries. Taking into account the on-site Coulomb repulsion U (where $U<<1$), the criterion for the stability of a topological insulator state is calculated at $t<<1$, $t\sim U$. Thus, in the case of $U>4\mathrm{\Delta }$, the topological insulator state, which is determined by chiral gapless edge modes in the gap Δ, is destroyed.     

Renormalization of non-semisimple gauge models with the background field method

We study the renormalization of non-semisimple gauge models quantized in the 't Hooft-background gauge to all orders. We analyze the normalization conditions for masses and couplings compatible with the Slavnov-Taylor and Ward-Takahashi Identities and with the IR constraints. We take into account both the problem of renormalization of CKM matrix elements and the problem of CP violation and we show that the Background Field Method (BFM) provides proper normalization conditions for fermion, scalar and gauge field mixings. We discuss the hard and the soft anomalies of the Slavnov-Taylor Identities and the conditions under which they are absent.     

Generating Majorana modes in one-dimensional p-wave superconductor with second-neighbor couplings by periodic kicking

Generating many Majorana modes (MMs) within one single system is a constructive method for experimental observation of MMs in condensed-matter systems. In this paper, we show that by adding periodic δ-function kicks on the chemical potential, a large number of MMs can be generated in the one-dimensional p-wave superconductor system with second-neighbor couplings. The Floquet theory has been used to analyze the stroboscopic properties and the winding number can be used to characterize the topological properties. We have analyzed the influence of the kicking parameters and second-neighbor couplings on the topological phase transitions.     

Effect of Floquet engineering on the p-wave superconductor with second-neighbor couplings

The influence of the Floquet engineering on a particular one-dimensional p-wave superconductor, Kitaev model, with second-neighbor couplings is investigated in this paper. The effective Hamiltonians in the rotated reference frames have been obtained, and the convergent regions of the approximated Hamiltonian as well as the topological phase diagrams have been analyzed and discussed. We show that by modulating the external driving field amplitude, frequency as well as the second-neighbor hopping amplitude, the rich phase diagrams and transitions between different topological phases can be obtained.     

用相对论平均场理论研究近滴线区原子核传统幻数的消失和新幻数的产生

提出了一种从理论上检验壳效应的方法.在考虑了由Bardeen，Cooper和Schrieffer提出的金属超导理论(BCS方法)的相对论平均场理论框架内，通过计算粒子数的涨落，发现涨落的大小和核的壳结构有紧密的关系，进而研究了滴线区一些传统幻数的消失和新幻数的产生. 关键词： 相对论平均场理论 粒子数涨落 幻数 壳效应     

Sub-pixel dimensional measurement with Logistic edge model

To separate substandard workpieces from products, sub-pixel edge location with Logistic edge model is proposed for dimensional measurement. In the first step, workpiece rotation is corrected with high precision image rotation to reduce the measurement error and simplify the edge model. Secondly, Logistic edge model is utilized for fitting the discrete edge data to locate the sub-pixel workpiece edge and model parameters are estimated through the objective function in terms of the difference between assumed model and real image data. Finally, an edge pixel compensation method is presented with edge pixel compensation value, which weakens the effect of edge transition zone effectively. Experimental results demonstrate that the proposed method is effective for dimensional measurement with the relative error less than 0.05%.     

A gauge theory for two-band model of Chern insulators and induced topological defects

In this paper a gauge theory is proposed for the two-band model of Chern insulators.Based on the so-calle't Hooft monopole model,a U(1)Maxwell electromagnetic sub-field is constructed from an SU(2)gauge field,from which arise two types of topological defects,monopoles and e2 merons.We focus on the topological number in the Hall conductance σ_xy=e²/hC,where C is the Chern number.It is discovered that in the monopole case C is indeterminate,while in the meron case C takes different values,due to a varying on-site energy m.As a typical example,we apply this method to the square lattice and compute the winding numbers(topological charges)of the defects;the C-evaluations we obtain reproduce the results of the usual literature.Furthermore,based on the gauge theory we propose a new model to obtain the high Chern numbers|C|=2,4.     

对数态Tavis-Cummings模型中辐射场的非经典性

本文研究了任意初态的双光子Tavis-Cummings模型的演化规律,作为例子,讨论了初始时刻两个原子均处于基态而光场为对数态时场的压缩效应,光子的聚束和反聚束效应.     

Loop calculations for the non-commutative U ⋆(1) gauge field model with oscillator term

The European Physical Journal C - Motivated by the success of the non-commutative scalar Grosse–Wulkenhaar model, a non-commutative U ⋆(1) gauge field theory including an...     

Multicritical behavior of the two-field Ginzburg-Landau model coupled to a gauge field

In this paper, we study the multicritical behavior of the Ginzburg-Landau model in a O(n₁)⊕O(n₂)-symmetric version containing (n₁/2+n₂/2)-complex order parameters coupled to a gauge field. We develop the RG analysis at a one-loop approximation in the context of the ?-expansion approach. The beta functions are obtained, and in the case of equal couplings between the two scalar fields and the gauge field and n₁=n₂=n/2, the infrared stability of the fixed points is discussed. It is found that the charged infrared-stable fixed point exists for n>393.2. Calculations of the relevant critical exponents are also carried out.     

一种碳纳米管场效应管的HSPICE模型

为在HSPICE中建立一种计算简单且精度较高的碳纳米管场效应管 (carbon nanotube field effect transistor, CNTFET) 模型, 在CNTFET半经典建模方法的基础上, 分析了自洽电势与载流子密度之间的关系, 提出用线性近似进行拟合, 并推导了自洽电势的显式表达式, 从而避免了积分方程的迭代求解过程. 然后在HSPICE中建立了相应的CNTFET模型, 通过仿真比较, 结果表明该模型具有较高的精度, 用其构建的逻辑门电路能够实现相应逻辑功能, 且运算时间大为减少. 关键词： 碳纳米管场效应管 半经典模型 线性近似拟合 HSPICE仿真     

Littlest Higgs模型中通过e^+e^-对撞研究新规范玻色子B_H与SM中规范玻色子的伴随产生过程

计划中的高能量、高亮度对撞机ILC在寻找新物理模型所预言的新的重粒子方面具有很大的潜力。本文,我们研究了在ILC上,通过过程e^+e^- ->r(Z)B_H发现littlest Higgs模型中最轻的新规范玻色子B_H的可能性。结果显示,在较大的参数空间范围,这两个过程都有较大的产生截面,能产生足够的信号探测B_H,尤其是对过程e^+e^- ->rB_H。另外,B_H的一些衰变道可以产生特征比较明显背景比较干净的信号。如果B_H存在,随着ILC的运行,新的规范玻色子B_H应能通过这两过程观测。