一维量子子自自旋链中拓扑有序态的物理描述

一维量子多体系统是凝聚态物理学中的重要研究方向之一,其中的新奇量子物态则是重要的研究课题。本文我们首先简要回顾一维量子整数自旋链体系的相关研究背景,然后提出一类SO(n)对称的严格可解量子自旋链模型及其矩阵乘积基态。当奇数n≥3时,体系的基态为Haldane相。利用这类态中隐藏的稀薄反铁磁序,我们找到了刻画这类态的非局域弦序参量,并在隐藏拓扑对称性的统一框架下解释了稀薄反铁磁序以及边缘态等奇特现象的起源。当偶数n≥4时,体系的基态为二聚化态。这些态属于破缺平移对称性的非Haldane相,但同样具有隐藏的反铁磁序。通过这些严格解的研究,我们还得到了一维SO(n)对称的双线性–双二次模型的基态相图,并发现在n≥5时,一维SO(n)对称的反铁磁海森堡模型的基态处于二聚化相中。基于以上这些结果,我们推广构造了一维平移不变且包含李群G对称性的Valence BondState(VBS)态,并利用其矩阵乘积表示讨论了对应哈密顿量的构造方法。对于自旋为S的量子整数自旋链,我们研究了两类具有不同拓扑属性的VBS类,前一类VBS态的边缘态处于SU(2)自旋J的不可约表示,后一类VBS态的边缘态为SO(2S+1)旋量。在前一类态中,我们以自旋为1的费米型VBS态为例构造了对应的哈密顿量。对后一类态,我们证明了它们等价于SO(2S+1)矩阵乘积态,从而揭示了呈展对称性的起源和边缘态的性质。我们还推广了SO(5)对称的玻色型和费米型VBS态,并探讨了它们的拓扑刻画方式。     

Effect of disorders on topological phases in one-dimensional optical superlattices

In a recent paper, Lang et al. proposed that edge states and topological phases can be observed in one-dimensional optical superlattices. They showed that the topological phases can be revealed by observing the density profile of a trapped fermion system, which displays plateaus with their positions. However, disorders are not considered in their model. To study the effect of disorders on the topological phases, we introduce random potentials to the model for optical superlattcies.Our calculations show that edge states are robust against the disorders. We find the edge states are very sensitive to the number of the sites in the optical superlattice and we propose a simple rule to describe the relationship between the edge states and the number of sites. The density plateaus are also robust against weak disorders provided that the average density is calculated over a long interval. The widths of the plateaus are proportional to the widths of the bulk energy gaps when there are disorders. The disorders can diminish the bulk energy gaps. So the widths of the plateaus decrease with the increase of disorders and the density plateaus disappear when disorders are too strong. The results in our paper can be used to guide the experimental detection of topological phases in one-dimensional systems.     

Solitary excitations in one-dimensional ferromagnetic spin chains with biquadratic exchange interaction

By using the traveling wave method, the solutions of the elliptic function wave and the solitary wave are obtained in a ferromagnetic spin chain with a biquadratic exchange interaction, a single ion anisotropic interaction and an anisotropic nearest neighbour interaction. The effects of the biquadratic exchange interaction and the single ion anisotropic interaction on the properties (width, peak and stability) of the soliton are investigated. It is also found that the effects vary with the strengths of these interactions.     

Spin accumulation and domain wall magnetoresistance in 35 nm Co wires

An enhancement of the resistance due to the presence of only one or two isolated domain walls is clearly evidenced by transport measurements in 35 nm epitaxial Co wires, 20 &mgr;m long. The deduced relative change in the resistivity is at least 1 order of magnitude larger than the one predicted from a model based on the mixing of spin channels occurring over the length scale of the domain wall width [P. M. Levy and S. Zhang, Phys. Rev. Lett. 79, 5110 (1997)]. This inconsistency can be resolved by taking the effect of spin accumulation into account, which scales in the case of Co over the much larger distance of the spin diffusion length.     

Domain wall theory of elementary excitations in anisotropic antiferromagneticS=1 chains

We present a theoretical investigation of elementary excitations in anisotropic antiferromagneticS=1 chains using the concept of domain walls in string (hidden) order. Domain walls are classified by the internal spin projectionS _dw ^z . We calculate energies and string correlation functions of low lying excited states of the domain wall type in the Haldane phase and compare the results to those of numerical computations. The boundaries of the Haldane phase are determined from the instability of these excitations with respect to the ground state. The interaction between two domain walls is found to be proportional to the productS _dw ^z , S _dw ^z ₂, it is effectively repulsive for equal spin projections.     

Domain wall theory of elementary excitations in anisotropic antiferromagneticS=1 chains

We present a theoretical investigation of elementary excitations in anisotropic antiferromagneticS=1 chains using the concept of domain walls in string (hidden) order. Domain walls are classified by the internal spin projectionS _dw ^z . We calculate energies and string correlation 0 functions of low lying excited states of the domain wall type in the Haldane phase and compare the results to those of numerical computations. The boundaries of the Haldane phase are determined from the instability of these excitations with respect to the ground state. The interaction between two domain walls is found to be proportional to the productS _dw ^z , S _dw ^z ₂, it is effectively repulsive 0140 for equal spin projections.     

Real-space observation of current-driven domain wall motion in submicron magnetic wires

We report direct observation of current-driven magnetic domain wall (DW) displacement by using a well-defined single DW in a microfabricated magnetic wire with submicron width. Magnetic force microscopy visualizes that a single DW introduced in a wire is displaced back and forth by positive and negative pulsed current, respectively. The direct observation gives quantitative information on the DW displacement as a function of the intensity and the duration of the pulsed current. The result is discussed in terms of the spin-transfer mechanism.     

Color image encoding in dual fractional Fourier-wavelet domain with random phases

A new cryptology in dual fractional Fourier-wavelet domain is proposed in this paper, which is calculated by discrete fractional Fourier transform and wavelet decomposition. Different random phases are used in different wavelet subbands in encryption. A new color image encoding method is also presented with basic color decomposition and encryption respectively. All the keys, including random phases and fractional orders in R, G and B three channels, should be correctly used in decryption, otherwise people cannot obtain the totally correct information. Some numerical simulations are presented to demonstrate the possibility of the method. It would have widely potential applications in digital color image processing and protection.     

Gapless excitations in strongly fluctuating superconducting wires

We study the low-temperature tunneling density of states of thin wires where superconductivity is destroyed through quantum phase-slip proliferation. Although this regime is believed to behave as an insulator, we show that for a large temperature range this phase is characterized by a conductivity falling off at most linearly with temperature, and has a gapless excitation spectrum. This novel conducting phase results from electron-electron interaction induced pair breaking. Also, it may help clarify the low-temperature metallic features found in films and wires whose bulk realization is superconducting.     

Spin excitations of a ferromagnetic wire with a magnetic domain wall

The spin excitation for a ferromagnetic wire with a domain wall (DW) is studied in a framework of the random phase approximation. We show that the excitation energy due to the DW is much smaller than that for the spin wave. In the spin-wave spectrum, there are lots of peaks or shoulders, which is related to the existence of the DW and the dimension of the leads. Using the results, the energy dissipation of conduction electrons is also discussed.     

Microwave-induced dephasing in one-dimensional metal wires

We report on the effect of monochromatic microwave (MW) radiation on the weak-localization corrections to the conductivity of quasi-one-dimensional silver wires. Because of the improved electron cooling in the wires, the MW-induced dephasing is observed without a concomitant overheating of electrons over wide ranges of the MW power P(MW) and frequency f. The observed dependences of the conductivity and MW-induced dephasing rate on P(MW) and f are in agreement with the theory by Altshuler, Aronov, and Khmelnitsky [Solid State Commun. 39, 619 (1981)]. Our results suggest that in the low-temperature experiments with 1D wires, saturation of the temperature dependence of the dephasing time can be caused by an MW electromagnetic noise with a sub-pW power.     

Spin and Majorana polarization in topological superconducting wires

We study a one-dimensional wire with strong Rashba and Dresselhaus spin-orbit coupling (SOC), which supports Majorana fermions when subject to a Zeeman magnetic field and in the proximity of a superconductor. Using both analytical and numerical techniques we calculate the electronic spin texture of the Majorana end states. We find that the spin polarization of these states depends on the relative magnitude of the Rashba and Dresselhaus SOC components. Moreover, we define and calculate a local "Majorana polarization" and "Majorana density" and argue that they can be used as order parameters to characterize the topological transition between the trivial system and the system exhibiting Majorana bound modes. We find that the local Majorana polarization is correlated to the transverse spin polarization, and we propose to test the presence of Majorana fermions in a 1D system by a spin-polarized density of states measurement.     

Dynamics of a domain wall and spin-wave excitations driven by a mesoscopic current

The dynamics of a domain wall driven by a spin-polarized current in a mesoscopic system is studied numerically. Spin mixing in the states of the conduction electrons is fully taken into account. When the Fermi energy of the electrons is larger than the exchange energy (E(F) > J(sd)), the spin precession induces spin-wave excitations in the local spins which contribute towards the displacement of the domain wall. The resulting average velocity is found to be much smaller than the one obtained in the adiabatic limit. For E(F) < J(sd), the results are consistent with the adiabatic approximation except for the region below the critical current where a residual domain wall velocity is found.     

Non-linear soliton excitations in antiferromagnetic chains

Topological excitations play a crucial role in antiferromagnetic chains. In the present review, we focus on the dynamical fluctuations induced by these quasi-particles, trying to show how they can be observed experimentally. In particular the pulsed nuclear magnetic resonance (NMR) technique can probe these fluctuations at very low frequency. In the same context, neutron spin echo (NSE) measurements are briefly mentioned. A discussion of soliton magnetic resonance (SMR) measurements in also presented: they reveal the existence of internal precessions in the solitons (Dyons) and they show that the uniform (q=0) soliton modes can be detected directly. The experimental data to be discussed were obtained on three compounds: TMMC which provides good examples for “broad” solitons and CsCoCl₃ for “narrow” solitons. A discussion of NMR data obtained with NENP is given in the context of the Haldane's conjecture. Member of Equipe de Recherche CNRS no. 216.     

Propagating vibrational excitations in molecular chains

We investigate quantum dynamics of vibrational excitations in one-dimensional (1D) molecular chain. Our model includes nearest neighbor interaction between identical molecular sites and one impurity atom placed in the middle (n = 0). We show that upon exciting the impurity site, its excess energy for relatively long for molecular scales time up to 100 ps is not redistributed uniformly among all other degrees of freedom. On the contrary an excitation propagates along the chain, reflected from the chain ends, and quantum interference of these waves yields to recurrence cycles and echo phenomena. For a critical cycle number k _c , echo components of the neighboring cycles start to overlap, and eventually for k ≫ k _c dynamics looks like chaotic one. The critical cycle number k _c depends on the coupling strength 0 ≤ C ≤ 1 of the impurity site with its neighbors n = ±1. k _c achieves the maximum for C ² = 1/2. Our results are in qualitative agreement with experimental data on vibrational excitations in various (CH₂) _n molecular chains, and besides offer a way for loss-free energy transfer between separated in space reaction centers.     

Strong-coupling topological Josephson effect in quantum wires

We investigate the Josephson effect for a setup with two lattice quantum wires featuring Majorana zero energy boundary modes at the tunnel junction. In the weak-coupling regime, the exact solution reproduces the perturbative result for the energy containing a contribution ～ ± cos(?/2) relative to the tunneling of paired Majorana fermions. As the tunnel amplitude g grows relative to the hopping amplitude w, the gap between the energy levels gradually diminishes until it closes completely at the critical value gc [Formula: see text]. At this point the Josephson energies have the principal values [Formula: see text], where m =- 1,0,1 and σ =± 1, a result not following from perturbation theory. It represents a transparent regime where three Bogoliubov states merge, leading to additional degeneracies of the topologically nontrivial ground state with an odd number of Majorana fermions at the end of each wire. We also obtain the exact tunnel currents for a fixed parity of the eigenstates. The Josephson current shows the characteristic 4π periodicity expected for a topological Josephson effect. We discuss the additional features of the current associated with a closure of the energy gap between the energy levels.