An important and incompletely answered question is whether a closed quantum system of many interacting particles can be localized by disorder. The time evolution of simple (unentangled) initial states is studied numerically for a system of interacting spinless fermions in one dimension described by the random-field XXZ Hamiltonian. Interactions induce a dramatic change in the propagation of entanglement and a smaller change in the propagation of particles. For even weak interactions, when the system is thought to be in a many-body localized phase, entanglement shows neither localized nor diffusive behavior but grows without limit in an infinite system: interactions act as a singular perturbation on the localized state with no interactions. The significance for proposed atomic experiments is that local measurements will show a large but nonthermal entropy in the many-body localized state. This entropy develops slowly (approximately logarithmically) over a diverging time scale as in glassy systems.

Many-body localization occurs in isolated quantum systems when Anderson localization persists in the presence of finite interactions. Despite strong evidence for the existence of a many-body localization transition, a reliable extraction of the critical disorder strength is difficult due to a large drift with system size in the studied quantities. In this Letter, we explore two entanglement properties that are promising for the study of the many-body localization transition: the variance of the half-chain entanglement entropy of exact eigenstates and the long time change in entanglement after a local quench from an exact eigenstate. We investigate these quantities in a disordered quantum Ising chain and use them to estimate the critical disorder strength and its energy dependence. In addition, we analyze a spin-glass transition at large disorder strength and provide evidence for it being a separate transition. We, thereby, give numerical support for a recently proposed phase diagram of many-body localization with localization protected quantum order [Huse et al., Phys. Rev. B 88, 014206 (2013).

We numerically calculate the conductivity σ of an undoped graphene sheet (size L) in the limit of vanishingly small lattice constant. We demonstrate one-parameter scaling for random impurity scattering and determine the scaling function β(σ) = d ln σ/d ln L. Contrary to a recent prediction, the scaling flow has no fixed point (β > 0) for conductivities up to and beyond the symplectic metalinsulator transition. Instead, the data supports an alternative scaling flow for which the conductivity at the Dirac point increases logarithmically with sample size in the absence of intervalley scattering -without reaching a scale-invariant limit.PACS numbers: 73.20.Fz, 73.20.Jc, 73.63.Nm Graphene provides a new regime for two-dimensional quantum transport [1,2,3], governed by the absence of backscattering of Dirac fermions [4]. A counterintuitive consequence is that adding disorder to a sheet of undoped graphene initially increases its conductivity [5,6]. Intervalley scattering at stronger disorder strengths enables backscattering [7], eventually leading to localization and to a vanishing conductivity in the thermodynamic limit [8,9]. Intervalley scattering becomes less and less important if the disorder is more and more smooth on the scale of the lattice constant a. The fundamental question of the new quantum transport regime is how the conductivity σ scales with increasing system size L if intervalley scattering is suppressed.In usual disordered electronic systems, the hypothesis of one-parameter scaling plays a central role in our conceptual understanding of the metal-insulator transition [10,11]. According to this hypothesis, the logarithmic derivative d ln σ/d ln L = β(σ) is a function only of σ itself [12] -irrespective of the sample size or degree of disorder. A positive β-function means that the system scales towards a metal with increasing system size, while a negative β-function means that it scales towards an insulator. The metal-insulator transition is at β = 0, β ′ > 0. In a two-dimensional system with symplectic symmetry, such as graphene, one would expect a monotonically increasing β-function with a metal-insulator transition at [13] σ S ≈ 1.4 (see Fig.

Weyl semimetals (WSMs) are topological quantum states wherein the electronic bands disperse linearly around pairs of nodes with fixed chirality, the Weyl points. In WSMs, nonorthogonal electric and magnetic fields induce an exotic phenomenon known as the chiral anomaly, resulting in an unconventional negative longitudinal magnetoresistance, the chiral-magnetic effect. However, it remains an open question to which extent this effect survives when chirality is not well-defined. Here, we establish the detailed Fermi-surface topology of the recently identified WSM TaP via combined angle-resolved quantum-oscillation spectra and band-structure calculations. The Fermi surface forms banana-shaped electron and hole pockets surrounding pairs of Weyl points. Although this means that chirality is ill-defined in TaP, we observe a large negative longitudinal magnetoresistance. We show that the magnetoresistance can be affected by a magnetic field-induced inhomogeneous current distribution inside the sample.

A direct signature of electron transport at the metallic surface of a topological insulator is the Aharonov-Bohm oscillation observed in a recent study of Bi2Se3 nanowires [Peng, Nature Mater. 9, 225 (2010)] where conductance was found to oscillate as a function of magnetic flux ϕ through the wire, with a period of one flux quantum ϕ0=h/e and maximum conductance at zero flux. This seemingly agrees neither with diffusive theory, which would predict a period of half a flux quantum, nor with ballistic theory, which in the simplest form predicts a period of ϕ0 but a minimum at zero flux due to a nontrivial Berry phase in topological insulators. We show how h/e and h/2e flux oscillations of the conductance depend on doping and disorder strength, provide a possible explanation for the experiments, and discuss further experiments that could verify the theory.

We propose an easily implemented approach to study time-dependent correlation functions of one dimensional systems at finite temperature T using the density matrix renormalization group. The entanglement growth inherent to any time-dependent calculation is significantly reduced if the auxiliary degrees of freedom which purify the statistical operator are time evolved with the physical Hamiltonian but reversed time. We exploit this to investigate the long time behavior of current correlation functions of the XXZ spin-1/2 Heisenberg chain. This allows a direct extraction of the Drude weight D at intermediate to large T . We find that D is nonzero -and thus transport is dissipationless -everywhere in the gapless phase. At low temperatures we establish an upper bound to D by comparing with bosonization.PACS numbers: 71.27.+a, 75.10.Pq, 75.40.Mg, 05.60.Gg It is an intriguing question if a physical system can exhibit dissipationless transport. In this case the conductivity has a singular contribution Dδ(ω) where D is typically referred to as the Drude weight. As a consequence, a fraction of an initially excited current will survive to infinite time. If the current operator is conserved by the Hamiltonian, the corresponding quantum system clearly supports dissipationless transport at any temperature T . The more subtle question of whether the Drude weight can be nonzero when the current operator has no overlap with any local conserved quantity has attracted considerable attention [1-18] without being resolved. In one spatial dimension it is believed that D = 0 is only possible at T > 0 for an integrable model where an infinite set of conserved local operators might restrict dissipation processes.This paper uses a finite-temperature time-dependent density matrix renormalization group (DMRG) approach to calculate the Drude weight for a prototypical integrable one-dimensional system -the antiferromagnetic XXZ Heisenberg chain. The latter describes L → ∞ interacting spin-1/2 degrees of freedom [24,25] and subsequently extended to address real-time dynamics [26][27][28][29]. In principle, it can be applied straightforwardly to nonzero T [30-32] by introducing auxiliary degrees of freedom to purify the thermal statistical operator [33]. In practice, however, the increase of entanglement with time has limited previous finite-temperature calculations to rather short timescales [10,34,35]. The second aim of our paper is to propose an easy-to-implement modification to the DMRG algorithm of Ref. 31: The auxiliaries are by construction inert, but they can be exposed to an arbitrary unitary transformation without involving any approximation. It turns out that the intuitive choice of time-evolving with the physical Hamiltonian but reversed time leads to a drastic reduction of the entanglement growth -thus, significantly longer timescales can be reached and the Drude weight of the XXZ chain can be calculated after all. This paper is organized as follows. We first explain our modified DMRG method and test it for the exactly solvab...

We show that the one-particle density matrix ρ can be used to characterize the interaction-driven many-body localization transition in closed fermionic systems. The natural orbitals (the eigenstates of ρ) are localized in the many-body localized phase and spread out when one enters the delocalized phase, while the occupation spectrum (the set of eigenvalues of ρ) reveals the distinctive Fockspace structure of the many-body eigenstates, exhibiting a step-like discontinuity in the localized phase. The associated one-particle occupation entropy is small in the localized phase and large in the delocalized phase, with diverging fluctuations at the transition. We analyze the inverse participation ratio of the natural orbitals and find that it is independent of system size in the localized phase. Introduction. While the theory of noninteracting disordered systems is well developed [1,2], the possibility of a localization transition in closed interacting systems has only recently been firmly established . This manybody localization (MBL) transition occurs at finite energy densities and is not a conventional thermodynamic transition [24,25]. Instead, it can be understood as a dynamical phase transition, associated with the emergence of a complete set of local conserved quantities in the localized phase, which thus behaves as an integrable system [26][27][28][29][30]. This restricts the entanglement entropy of the eigenstates to an area law [31], in contrast to the volume law predicted by the eigenstate thermalization hypothesis for the ergodic delocalized phase [32][33][34]. At the localization transition, the fluctuations of the entanglement entropy diverge [16,35]. The effects of MBL are also observed in the dynamics following, for example, a global quench from a product state, wherein dephasing between the effective degrees of freedom leads to a characteristic logarithmic growth of the entanglement entropy [6,10,12]. These features comprise a much richer set of signatures than in the context of noninteracting systems, for which, in the spirit of one-parameter scaling, the notion of a localization length based on single-particle wave functions generally suffices [1,2].

A potential step in a graphene nanoribbon with zigzag edges is shown to be an intrinsic source of intervalley scattering -no matter how smooth the step is on the scale of the lattice constant a. The valleys are coupled by a pair of localized states at the opposite edges, which act as an attractor/repellor for edge states propagating in valley K/K ′ . The relative displacement ∆ along the ribbon of the localized states determines the conductance G. Our result G = (e 2 /h)[1−cos(N π+ 2π∆/3a)] explains why the "valley-valve" effect (the blocking of the current by a p-n junction) depends on the parity of the number N of carbon atoms across the ribbon.