Classical impurities and boundary Majorana zero modes in quantum chains

We study the response of classical impurities in quantum Ising chains. The Z₂${\mathbb{Z}}_2$ degeneracy they entail renders the existence of two decoupled Majorana modes at zero energy, an exact property of a finite system at arbitrary values of its bulk parameters. We trace the evolution of these modes across the transition from the disordered phase to the ordered one and analyze the concomitant qualitative changes of local magnetic properties of an isolated impurity. In the disordered phase, the two ground states differ only close to the impurity, and they are related by the action of an explicitly constructed quasi-local operator. In this phase the local transverse spin susceptibility follows a Curie law. The critical response of a boundary impurity is logarithmically divergent and maps to the two-channel Kondo problem, while it saturates for critical bulk impurities, as well as in the ordered phase. The results for the Ising chain translate to the related problem of a resonant level coupled to a 1d p-wave superconductor or a Peierls chain, whereby the magnetic order is mapped to topological order. We find that the topological phase always exhibits a continuous impurity response to local fields as a result of the level repulsion of local levels from the boundary Majorana zero mode. In contrast, the disordered phase generically features a discontinuous magnetization or charging response. This difference constitutes a general thermodynamic fingerprint of topological order in phases with a bulk gap.     

Néel order in doped quasi-one-dimensional antiferromagnets

We study the Néel temperature of quasi-one-dimensional S = 1/2 antiferromagnets containing nonmagnetic impurities. We first consider the temperature dependence of the staggered susceptibility of finite chains with open boundary conditions, which shows an interesting difference for even and odd length chains. We then use a mean field theory treatment to incorporate the three-dimensional interchain couplings. The resulting Néel temperature shows a pronounced drop as a function of doping by up to a factor of 5.     

耦合电磁场对石墨烯量子磁振荡的影响

我们研究了包含自旋轨道耦合与杂质散射在内的石墨烯量子磁振荡对外加电磁场的响应.我们发现,石墨烯中自旋轨道耦合、电磁场以及边界共同修正了朗道能谱,且当电场与磁场比值超过某一临界值时,量子磁振荡会突然消失,这与非相对论二维电子气的情况显著不同.这种现象可以通过朗道量子化轨道由封闭转化为开放的半经典理论来解释.此外,我们还发现杂质散射和温度的共同作用会使得磁振荡振幅衰减.我们的结果可用于分析石墨烯及其类似结构(硅烯、锗烯、锡烯等)的费米能级与朗道能谱的相互作用,进而探测自旋轨道耦合引起的能隙.     

Boundary susceptibility in the spin-1/2 chain: Curie-like behavior without magnetic impurities

We investigate the low-temperature thermodynamics of the spin-1/2 Heisenberg chain with open ends. On the basis of boundary conformal field theory arguments and numerical density matrix renormalization group calculations, it is established that in the isotropic case the impurity susceptibility exhibits a Curie-like divergent behavior as the temperature decreases, even in the absence of magnetic impurities. A similar singular temperature dependence is also found in the boundary contributions of the specific heat coefficient. In the anisotropic case, for 1/2相似文献   

EPR study of the low temperature charge density wave state of o-TaS3

We report an EPR study of the chain conductor o-TaS₃ in the low temperature charge density wave (CDW) state. The EPR spectrum is attributed to Fe³⁺ (S=5/2) impurities. A power law for the temperature dependence of the EPR intensity, (T^−α with an exponent α∼0.8) found below ∼30 K is very close to that previously found in magnetic susceptibility measurements. The possible role of these impurities in the susceptibility data are discussed.     

Finite-size effects in single chain magnets: an experimental and theoretical study

The problem of finite-size effects in s=1/2 Ising systems showing slow dynamics of the magnetization is investigated introducing diamagnetic impurities in a Co2+-radical chain. The static magnetic properties have been measured and analyzed considering the peculiarities induced by the ferrimagnetic character of the compound. The dynamic susceptibility shows that an Arrhenius law is observed with the same energy barrier for the pure and the doped compounds while the prefactor decreases, as theoretically predicted. Multiple spin reversal has also been investigated.     

Fractional impurity moments in two-dimensional noncollinear magnets

We study dilute magnetic impurities and vacancies in two-dimensional frustrated magnets with noncollinear order. Taking the triangular-lattice Heisenberg model as an example, we use quasiclassical methods to determine the impurity contributions to the magnetization and susceptibility. Most importantly, each impurity moment is not quantized but receives nonuniversal screening corrections due to local relief of frustration. At finite temperatures, where bulk long-range order is absent, this implies an impurity-induced magnetic response of Curie form, with a prefactor corresponding to a fractional moment per impurity. We also discuss the behavior in an applied magnetic field, where we find a singular linear-response limit for overcompensated impurities.     

Finite size effects around pseudo-transition in one-dimensional models with nearest neighbor interaction

Recently gigantic peaks in thermodynamic response functions have been observed at finite temperature for one-dimensional models with short-range coupling, closely resembling a second-order phase transition. Thus, we will analyze the finite temperature pseudo-transition property observed in some one-dimensional models and its relationship with finite size effect. In particular, we consider two chain models to study the finite size effects; these are the Ising-Heisenberg tetrahedral chain and an Ising-Heisenberg-type ladder model. Although the anomalous peaks of these one-dimensional models have already been studied in the thermodynamic limit, here we will discuss the finite size effects of the chain and why the peaks do not diverge in the thermodynamic limit. So, we discuss the dependence of the finite size effects, for moderately and sufficiently large systems, in which the specific heat and magnetic susceptibility exhibit peculiar rounded towering peaks for a given temperature. This behavior is quite similar to a continuous phase transition, but there is no singularity. For moderately large systems, the peaks narrow and increase in height as the number of unit cells is increased, and the location of peak shifts slightly. Hence, one can naively induce that the sharp peak should lead to a divergence in the thermodynamic limit. However, for a rather large system, the height of a peak goes asymptotically to a finite value. Our result rigorously confirms the dependence of the peak height with the number of unit cells at the pseudo-critical temperature. We also provide an alternative empirical function that satisfactorily fits specific heat and magnetic susceptibility at pseudo-critical temperature. Certainly, our result is crucial to understand the finite size correction behavior in quantum spin models, which in general are only numerically tractable within the framework of the finite size analysis.     

A Bijection Theorem for Domino Tilings with Diagonal Impurities

We consider the dimer problem on a planar non-bipartite graph G, where there are two types of dimers one of which we regard as impurities. Computer simulations reveal a reminiscence of the Cheerios effect, that is, impurities are attracted to the boundary, which is the motivation to study this particular graph. Our main theorem is a variant of the Temperley bijection: a bijection between the set of dimer coverings and the set of spanning forests with certain conditions. We further discuss some implications of this theorem: (1) the local move connectedness yielding an ergodic Markov chain on the set of all possible dimer coverings, and (2) a rough bound for the number of dimer coverings and that for the probability of finding an impurity at a given edge, which is an extension of a result in (Nakano and Sadahiro in ).     

Exact and numerical results for a dimerized coupled spin- 1/2 chain

We establish exact results for coupled spin-1/2 chains for special values of the four-spin interaction V and dimerization parameter delta. The first exact result is at delta = 1/2 and V = -2. Because we find a very small but finite gap in this dimerized chain, this can serve as a very strong test case for numerical and approximate analytical techniques. The second result is for the homogeneous chain with V = -4 and gives evidence that the system has a spontaneously dimerized ground state. Numerical diagonalization and bosonization techniques indicate that the interplay between dimerization and interaction could result in gapless phases in the regime 0相似文献   

Insulating phases and superfluid-insulator transition of disordered boson chains

Using a strong disorder real-space renormalization group, we study the phase diagram of a fully disordered chain of interacting bosons. Since this approach does not suffer from runaway flows, it allows a direct study of the insulating phases, not accessible in a weak disorder perturbative treatment. We find that the universal properties of the insulating phase are determined by the details and symmetries of the on-site chemical-potential disorder. Three insulating phases are possible: (i) an incompressible Mott glass with a finite superfluid susceptibility, (ii) a random-singlet glass with diverging compressibility and superfluid susceptibility, (iii) a Bose glass with a finite compressibility but diverging superfluid susceptibility. In addition to characterizing the insulating phases, we show that the superfluid-insulator transition is always described by Kosterlitz-Thouless-like flows.     

具有长程相互作用S-1/2 XY链的研究

采用平均场Jordan - Wigner 变换分析方法,研究了外场中且具有Z方向均匀长程相互作用自旋－1/2 XY链的热力学性质,得到了系统格点的亥姆赫兹自由能、内能、比热、磁化强度、磁化率等热力学量的解析表达式及其数值解,讨论了系统的一级和两级相变,数值结果在退化条件下与其他文献的结果符合很好. 关键词： XY链')" href="#">XY链 平均场Jordan-Wigner变换 长程相互作用     

Localization of polymers in a finite medium with fixed random obstacles

In this paper we investigate the conformation statistics of a Gaussian chain embedded in a medium of finite size, in the presence of quenched random obstacles. The similarities and differences between the case of random obstacles and the case of a Gaussian random potential are elucidated. The connection with the density of states of electrons in a metal with random repulsive impurities of finite range is discussed. We also interpret the results obtained in some previous numerical simulations. Received 14 August 2001     

Band structures of bilayer graphene superlattices

We formulate a low energy effective Hamiltonian to study superlattices in bilayer graphene (BLG) using a minimal model which supports quadratic band touching points. We show that a one dimensional (1D) periodic modulation of the chemical potential or the electric field perpendicular to the layers leads to the generation of zero-energy anisotropic massless Dirac fermions and finite energy Dirac points with tunable velocities. The electric field superlattice maps onto a coupled chain model comprised of "topological" edge modes. 2D superlattice modulations are shown to lead to gaps on the mini-Brillouin zone boundary but do not, for certain symmetries, gap out the quadratic band touching point. Such potential variations, induced by impurities and rippling in biased BLG, could lead to subgap modes which are argued to be relevant to understanding transport measurements.     

Order by disorder from nonmagnetic impurities in a two-dimensional quantum spin liquid

We consider doping of nonmagnetic impurities in the spin-1/2, 1/5-depleted square lattice. This structure, whose undoped phase diagram offers both magnetically ordered and spin-liquid ground states, is realized physically in CaV4O9. Doping into the ordered phase results in a progressive loss of order, which becomes complete at the percolation threshold. By contrast, doping into the spin liquids creates a phase of weak but long-ranged antiferromagnetic order, a true order-by-disorder phenomenon. We study the phase diagram of the doped system by computing the static susceptibility and staggered magnetization using a stochastic series-expansion quantum Monte Carlo technique.     

Quasi-particle properties in a quasi-two-dimensional electron liquid

We consider the quasi-particle properties such as the effective mass and spin susceptibility of quasi-two-dimensional electron systems. The finite quantum well width effects are incorporated into the local-field factors that describe the charge and spin correlations. We employ the Fermi-hypernetted chain formalism in conjunction with fluctuation-dissipation theorem to obtain the local-field factors. Our results are in good agreement with recent experiments.      

First passage time distributions for finite one-dimensional random walks

We present closed expressions for the characteristic function of the first passage time distribution for biased and unbiased random walks on finite chains and continuous segments with reflecting boundary conditions. Earlier results on mean first passage times for one-dimensional random walks emerge as special cases. The divergences that result as the boundary is moved out to infinity are exhibited explicitly. For a symmetric random walk on a line, the distribution is an elliptic theta function that goes over into the known Lévy distribution with exponent 1/2 as the boundary tends to ∞.     

Zero-modes and thermodynamics of disordered spin-1/2 ladders

The influence of non-magnetic doping on the thermodynamic properties of two-leg S = 1/2 spin ladders is studied in this paper. It is shown that, for a weak interchain coupling, the problem can be mapped onto a model of random mass Dirac (Majorana) fermions. We investigate in detail the structure of the fermionic states localized at an individual mass kink (zero-modes) in the framework of a generalized Dirac model. The low-temperature thermodynamic properties are dominated by these zero-modes. We use the single-fermion density of states, known to exhibit the Dyson singularity in the zero-energy limit, to construct the thermodynamics of the spin ladder. In particular, we find that the magnetic susceptibility χ diverges at T → 0 as 1/T ln²(1/T), and the specific heat behaves as C 1/ln³(1/T). The predictions on magnetic susceptibility are consistent with the most recent results of quantum Monte Carlo simulations on doped ladders with randomly distributed impurities. We also calculate the average staggered magnetic susceptibility induced in the system by such defects.     

Effect of laser intensity on the semiconductor–metal transition in a doped Quantum Well

We demonstrate laser induced semiconductor–metal transition through an abrupt change in diamagnetic susceptibility of a donor at critical concentration in a GaAs/Al_xGa_1−xAs Quantum Well for finite barrier model in the effective mass approximation using variational principle. We have considered Anderson‘s localization due to the random distribution of impurities in our calculation. The nonparabolicity of the conduction band is also considered. Our results without laser field agree with the earlier theoretical results and also with the recent experimental results.     

Full-band extended states with random phases in one-dimensional disordered system with specific impurities

We investigate transport properties of electrons in a one-dimensional (1D) disordered system consisting of a host chain attached with specific impurities. Every impurity, labelled by j and possessing site energy , is side-coupled to two adjacent sites of the host chain with hopping integral t _1j and changesthe original nearest-neighbor (NN) hopping to t _2j . We show that if and for all impurities, with t ₀ being the NN hopping of the host chain, the states in the whole band are extended, even though s and positions of impurities are random. The phases of these states, however, are spatially random, corresponding to finite free path and infinite localization length in such a 1D system.Received: 6 May 2004, Published online: 12 July 2004PACS: 72.15.Rn Localization effects (Anderson or weak localization) - 72.80.Ng Disordered solids - 73.20.Jc Delocalization processes