Random field effects in field-driven quantum critical points

We investigate the role of disorder for field-driven quantum phase transitions of metallic antiferromagnets. For systems with sufficiently low symmetry, the combination of a uniform external field and non-magnetic impurities leads effectively to a random magnetic field which strongly modifies the behavior close to the critical point. Using perturbative renormalization group, we investigate in which regime of the phase diagram the disorder affects critical properties. In heavy fermion systems where even weak disorder can lead to strong fluctuations of the local Kondo temperature, the random field effects are especially pronounced. We study possible manifestation of random field effects in experiments and discuss in this light neutron scattering results for the field driven quantum phase transition in CeCu_5.8Au_0.2.     

Disorder-induced quantum-Griffiths-like features from a non-conventional renormalization group analysis near four dimensions

We investigate the role played by symmetry conserving quenched disorder on quantum criticality of a variety of d-dimensional systems with a continuous symmetry order parameter. We employ a non-standard procedure which combines a preliminary reduction to an effective classical random problem and a successive conventional renormalization group treatment. Solving the effective flow equations to first order in ε=4−d and then restoring the original coupling parameters, for d<4 we find a quantum critical point scenario exhibiting unusual features, which remind us of some predictions of the quantum Griffiths phase model.     

Phase diagram of the random Heisenberg antiferromagnetic spin-1 chain

We present a new perturbative real space renormalization group (RG) to study random quantum spin chains and other one-dimensional disordered quantum systems. The method overcomes problems of the original approach which fails for quantum random chains with spins larger than S=1/2. Since it works even for weak disorder, we are able to obtain the zero temperature phase diagram of the random antiferromagnetic Heisenberg spin-1 chain as a function of disorder. We find a random singlet phase for strong disorder. As the disorder decreases, the system shows a crossover from a Griffiths to a disordered Haldane phase.     

On the temperature dependence of the dielectric susceptibility in quantum ferroelectrics

The results of the renormalization group investigation performed previously by the author to the study of the quantum critical behaviour of the transverse Ising model are now adopted to the phase transition in quantum ferroelectrics. The temperature dependence of dielectric susceptibility ϵ is calculated for three-dimensional systems near the quantum limit. The formula for ϵ reproduces the quantum as well as the classical behaviour near the critical temperature.     

Griffiths-McCoy singularities in random quantum spin chains: exact results through renormalization

The Ma-Dasgupta-Hu renormalization group (RG) scheme is used to study singular quantities in the Griffiths phase of random quantum spin chains. For the random transverse-field Ising spin chain we have extended Fisher's analytical solution to the off-critical region and calculated the dynamical exponent exactly. Concerning other random chains we argue by scaling considerations that the RG method generally becomes asymptotically exact for large times, both at the critical point and in the whole Griffiths phase. This statement is checked via numerical calculations on the random Heisenberg and quantum Potts models by the density matrix renormalization group method.     

Critical behaviour of random compressible magnets

The critical properties of a compressible random magnet are studied using renormalization group methods. Then-component orderparameter is coupled to quenched disorder and to the elastic fluctuations of the anisotropic solid. It is shown, that the critical behaviour of a compressible random magnet is in general the same as that of a random magnet on a rigid lattice. However, if the specific heat exponent of the ideal magnet is positive and the disorder is sufficiently weak, a macroscopic instability may prevent the system in reaching the critical point. The resulting first-order transition may be preceded by pseudocritical behaviour characteristic to pure compressible magnets. The effect of random magnetic fields on the critical properties of compressible magnets is also discussed.     

量子多体系统的线性张量重正化群方法

文章简述了数值重正化群方法的历史发展,包括威耳逊（Wilson）的数值重正化群算法,S.R.White的密度矩阵重正化群方法,以及近期迅速发展的处理强关联量子系统的几种张量网络态与张量网络算法.在此基础上,文章重点介绍了作者最近提出的用于研究量子多体系统热力学性质的线性张量重正化群方法,以及该方法在一维和二维量子系统中的应用.     

Spin dynamics in hole-doped two-dimensional S = 1/2 Heisenberg antiferromagnets: 63Cu NQR relaxation in La2-xSrxCuO4 for x ≤ 0.04

A cluster algorithm formulated in continuous (imaginary) time is presented for Ising models in a transverse field. It works directly with an infinite number of time-slices in the imaginary time direction, avoiding the necessity to take this limit explicitly. The algorithm is tested at the zero-temperature critical point of the pure two-dimensional (2d) transverse Ising model. Then it is applied to the 2d Ising ferromagnet with random bonds and transverse fields, for which the phase diagram is determined. Finite size scaling at the quantum critical point as well as the study of the quantum Griffiths-McCoy phase indicate that the dynamical critical exponent is infinite as in 1d. Received 6 November 1998     

Transport through quantum dots: a combined DMRG and embedded-cluster approximation study

The numerical analysis of strongly interacting nanostructures requires powerful techniques. Recently developed methods, such as the time-dependent density matrix renormalization group (tDMRG) approach or the embedded-cluster approximation (ECA), rely on the numerical solution of clusters of finite size. For the interpretation of numerical results, it is therefore crucial to understand finite-size effects in detail. In this work, we present a careful finite-size analysis for the examples of one quantum dot, as well as three serially connected quantum dots. Depending on “odd-even” effects, physically quite different results may emerge from clusters that do not differ much in their size. We provide a solution to a recent controversy over results obtained with ECA for three quantum dots. In particular, using the optimum clusters discussed in this paper, the parameter range in which ECA can reliably be applied is increased, as we show for the case of three quantum dots. As a practical procedure, we propose that a comparison of results for static quantities against those of quasi-exact methods, such as the ground-state density matrix renormalization group (DMRG) method or exact diagonalization, serves to identify the optimum cluster type. In the examples studied here, we find that to observe signatures of the Kondo effect in finite systems, the best clusters involving dots and leads must have a total z-component of the spin equal to zero.     

Realization of quantum walks with negligible decoherence in waveguide lattices

Quantum random walks are the quantum counterpart of classical random walks, and were recently studied in the context of quantum computation. Physical implementations of quantum walks have only been made in very small scale systems severely limited by decoherence. Here we show that the propagation of photons in waveguide lattices, which have been studied extensively in recent years, are essentially an implementation of quantum walks. Since waveguide lattices are easily constructed at large scales and display negligible decoherence, they can serve as an ideal and versatile experimental playground for the study of quantum walks and quantum algorithms. We experimentally observe quantum walks in large systems ( approximately 100 sites) and confirm quantum walks effects which were studied theoretically, including ballistic propagation, disorder, and boundary related effects.     

The Depinning Transition in Presence of Disorder: A Toy Model

We introduce a toy model, which represents a simplified version of the problem of the depinning transition in the limit of strong disorder. This toy model can be formulated as a simple renormalization transformation for the probability distribution of a single real variable. For this toy model, the critical line is known exactly in one particular case and it can be calculated perturbatively in the general case. One can also show that, at the transition, there is no fixed distribution accessible by renormalization which corresponds to a disordered fixed point. Instead, both our numerical and analytic approaches indicate a transition of infinite order (of the Berezinskii–Kosterlitz–Thouless type). We give numerical evidence that this infinite order transition persists for the problem of the depinning transition with disorder on the hierarchical lattice.     

External field induced chaos in an infinite square well potential

We study the motion of a particle in an infinite square well potential in the presence of a monochromatic external field. The equations of motion of this system have a particularly simple structure compared to other driven nonlinear systems, and yet the system exhibits a transition to chaotic behavior. The critical amplitudes of the external field where ‘breakdown’ of KAM invariants occurs and large scale chaos sets in are computed by numerical experiment. They are found to be in good agreement with predictions based on a renormalization group scheme.     

Exploiting quantum parallelism to simulate quantum random many-body systems

We present an algorithm that exploits quantum parallelism to simulate randomness in a quantum system. In our scheme, all possible realizations of the random parameters are encoded quantum mechanically in a superposition state of an auxiliary system. We show how our algorithm allows for the efficient simulation of dynamics of quantum random spin chains with known numerical methods. We propose an experimental realization based on atoms in optical lattices in which disorder could be simulated in parallel and in a controlled way through the interaction with another atomic species.     

Theory of smeared quantum phase transitions

We present an analytical strong-disorder renormalization group theory of the quantum phase transition in the dissipative random transverse-field Ising chain. For Ohmic dissipation, we solve the renormalization flow equations analytically, yielding asymptotically exact results for the low-temperature properties of the system. We find that the interplay between quantum fluctuations and Ohmic dissipation destroys the quantum critical point by smearing. We also determine the phase diagram and the behavior of observables in the vicinity of the smeared quantum phase transition.     

Effect of disorder on two-dimensional wetting

For the problem of the 2D wetting transition near a 1D random wall, we show by a renormalization calculation that the effect of disorder is marginally relevant. It is therefore expected that the nature of the wetting transition and the location of the critical point are modified by any amount of disorder. This is supported by numerical simulations based on transfer matrix calculations. We investigate also the problem of wetting near a random wall on hierarchical lattices and find similar results.     

Dynamical conductivity at the dirty superconductor-metal quantum phase transition

We study the transport properties of ultrathin disordered nanowires in the neighborhood of the superconductor-metal quantum phase transition. To this end we combine numerical calculations with analytical strong-disorder renormalization group results. The quantum critical conductivity at zero temperature diverges logarithmically as a function of frequency. In the metallic phase, it obeys activated scaling associated with an infinite-randomness quantum critical point. We extend the scaling theory to higher dimensions and discuss implications for experiments.     

一维自旋1键交替XXZ链中的量子纠缠和临界指数

利用基于张量网络表示的矩阵乘积态算法以及无限虚时间演化块抽取方法,本文研究了一维无限格点自旋1的键交替反铁磁XXZ海森伯模型中的量子相变.分别计算了系统的von Neumann熵、单位格点保真度和序参量,从而得到了系统随键交替强度的变化从拓扑有序Néel相到局域有序二聚化相的量子相变点.我们用矩阵乘积态方法拟合出了相变的中心荷c?0.5,表明此相变属于二维经典的Ising普适类.另外,通过对拓扑Néel序的数值拟合,我们得到了相变点处的特征临界指数β′=0.236和γ′=0.838.     

Scaling theory and finite systems

A renormalization group transformation is introduced with the help of which critical properties of infinite systems can be related to finite systems. As a numerical example the method is applied to the two-dimensional Ising model. The critical point and critical point exponent are computed in addition to the amplitude of the logarithmic singularity in the specific heat.     

Monogamy quantum correlation near the quantum phase transitions in the two-dimensional XY spin systems

We investigate the role of quantum correlation around the quantum phase transitions by using quantum renormalization group theory. Numerical analysis indicates that quantum correlation as well as quantum nonlocality can efficiently detect the quantum critical point in the two-dimensional XY systems. The nonanalytic behavior of the first derivative of quantum correlation is observed at the critical point as the size of the model increases. Furthermore, we discuss the quantum correlation distribution in this system based on the square of concurrence(SC) and square of quantum discord(SQD). The monogamous properties of SC and SQD are obtained. Particularly, we prove that the quantum critical point can also be achieved by monogamy score.     

Renormalized tricritical behaviour for wetting transitions

In this paper we study tricritical wetting behaviour in three dimensions. In particular we concentrate on systems with short-ranged forces and apply linear functional renormalization group techniques to elucidate the effect of fluctuations upon tricriticality. In comparison with studies of critical wetting we identify an additional fluctuation regime which is relevant for values of the capillary parameter between 2/9 and 1/2. We demonstrate that this regime essentially provides a crossover from mean-field like behaviour, in which tricritical exponents are always distinct from their critical counterparts, from intermediate- and strong-fluctuation behaviour where the critical exponents for tricritical and critical wetting are found to always coincide. We conclude by discussing briefly the possible relevance of these results for experimental studies of wetting. Received 4 January 2001 and Received in final form 11 May 2001