Localisation versus self-trapping: Polaron formation in the Anderson-Holstein model
We discuss polaron formation in disordered electron-phonon systems.
cond-mat.str-el↗
arXiv subjects
Holger Fehske
Publications and source records attributed to Holger Fehske.
Quantum phase transitions in one-dimensional electron-phonon systems
We discuss the Luttinger-liquid charge-density-wave and Peierls-insulator Mott-insulator quantum phase transitions in 1D electron-phonon systems.
cond-mat.str-el↗
Spectral signatures of Holstein polarons
We review numerical results for ground-state and spectral properties of the single-electron Holstein model.
cond-mat.str-el↗
The Kernel Polynomial Method
Efficient and stable algorithms for the calculation of spectral quantities and correlation functions are some of the key tools in computational condensed matter physics. In this article we review basic properties and recent developments of Chebyshev expansion based algorithms and the Kernel Polynomial Method. Characterized by a resource consumption that scales linearly with the problem dimension these methods enjoyed growing popularity over the last decade and found broad application not only in physics. Representative examples from the fields of disordered systems, strongly correlated electrons, electron-phonon interaction, and quantum spin systems we discuss in detail. In addition, we illustrate how the Kernel Polynomial Method is successfully embedded into other numerical techniques, such as Cluster Perturbation Theory or Monte Carlo simulation.
cond-mat.other↗
Local distribution approach to disordered binary alloys
We study the electronic structure of the binary alloy and (quantum) percolation model. Our study is based on a self-consistent scheme for the distribution of local Green functions. We obtain detailed results for the density of states, from which the phase diagram of the binary alloy model is constructed, and discuss the existence of a quantum percolation threshold.
cond-mat.str-el↗
Many-polaron problem by cluster perturbation theory
The carrier-density dependence of the photoemission spectrum of the Holstein many-polaron model is studied using cluster perturbation theory combined with an improved cluster diagonalization by Chebychev expansion.
cond-mat.str-el↗
Comparative numerical study of Anderson localization in disordered electron systems
Taking into account that a proper description of disordered systems should focus on distribution functions, the authors develop a powerful numerical scheme for the determination of the probability distribution of the local density of states (LDOS), which is based on a Chebyshev expansion with kernel polynomial refinement and allows the study of large finite clusters (up to $100^3$). For the three-dimensional Anderson model it is demonstrated that the distribution of the LDOS shows a significant change at the disorder induced delocalisation-localisation transition. Consequently, the so-called typical density of states, defined as the geometric mean of the LDOS, emerges as a natural order parameter. The calculation of the phase diagram of the Anderson model proves the efficiency and reliability of the proposed approach in comparison to other localisation criteria, which rely, e.g., on the decay of the wavefunction or the inverse participation number.
cond-mat.dis-nn↗
Microscopic modelling of doped manganites
Colossal magneto-resistance manganites are characterised by a complex interplay of charge, spin, orbital and lattice degrees of freedom. Formulating microscopic models for these compounds aims at meeting to conflicting objectives: sufficient simplification without excessive restrictions on the phase space. We give a detailed introduction to the electronic structure of manganites and derive a microscopic model for their low energy physics. Focussing on short range electron-lattice and spin-orbital correlations we supplement the modelling with numerical simulations.
cond-mat.str-el↗
Optical response of electrons in a random potential
Using our recently developed Chebyshev expansion technique for finite-temperature dynamical correlation functions we numerically study the AC conductivity $σ(ω)$ of the Anderson model on large cubic clusters of up to $100^3$ sites. Extending previous results we focus on the role of the boundary conditions and check the consistency of the DC limit, $ω\to 0$, by comparing with direct conductance calculations based on a Greens function approach in a Landauer Büttiker type setup.
cond-mat.dis-nn↗
Unusual localisation effects in quantum percolation
We present a detailed study of the quantum site percolation problem on simple cubic lattices, thereby focussing on the statistics of the local density of states and the spatial structure of the single particle wavefunctions. Using the Kernel Polynomial Method we refine previous studies of the metal-insulator transition and demonstrate the non-monotonic energy dependence of the quantum percolation threshold. Remarkably, the data indicates a ``fragmentation'' of the spectrum into extended and localised states. In addition, the observation of a chequerboard-like structure of the wavefunctions at the band centre can be interpreted as anomalous localisation.
cond-mat.str-el↗
Delocalisation transition in chains with correlated disorder
We show that in the one-dimensional (1D) Anderson model long-range correlations within the sequence of on-site potentials may lead to a region of extended states in the vicinity of the band centre, i.e., to a correlation-induced insulator-metal transition. Thus, although still disordered, the 1D system can behave as a conductor.
cond-mat.str-el↗
Spin-lattice coupling effects in the Holstein double-exchange model
Based on the Holstein double-exchange model and a highly efficient single cluster Monte Carlo approach we study the interplay of double-exchange and polaron effects in doped colossal magneto-resistance (CMR) manganites. The CMR transition is shown to be appreciably influenced by lattice polaron formation.
cond-mat.str-el↗
Anderson localization in strongly coupled disordered electron-phonon systems
Based on the statistical dynamical mean field theory, we investigate, in a generic model for a strongly coupled disordered electron-phonon system, the competition between polaron formation and Anderson localization. The statistical dynamical mean field approximation maps the lattice problem to an ensemble of self-consistently embedded impurity problems. It is a probabilistic approach, focusing on the distribution instead of the average values for observables of interest. We solve the self-consistent equations of the theory with a Monte-Carlo sampling technique, representing distributions for random variables by random samples, and discuss various ways to determine mobility edges from the random sample for the local Green function. Specifically, we give, as a function of the `polaron parameters', such as adiabaticity and electron-phonon coupling constants, a detailed discussion of the localization properties of a single polaron, using a bare electron as a reference system.
cond-mat.str-el↗
Entanglement and correlation in anisotropic quantum spin systems
Analytical expressions for the entanglement measures concurrence, i-concurrence and 3-tangle in terms of spin correlation functions are derived using general symmetries of the quantum spin system. These relations are exploited for the one-dimensional XXZ-model, in particular the concurrence and the critical temperature for disentanglement are calculated for finite systems with up to six qubits. A recent NMR quantum error correction experiment is analyzed within the framework of the proposed theoretical approach.
quant-ph↗
Lattice and superexchange effects in doped CMR manganites
We report on the influence of the lattice degrees of freedom on charge, orbital and spin correlations in colossal magnetoresistance (CMR) manganites. For the weakly doped compounds we demonstrate that the electron-phonon coupling promotes the trapping of charge carriers, the disappearance of the orbital polaron pattern and the breakdown of ferromagnetism at the CMR transition. The role of different superexchange interactions is explored.
cond-mat.str-el↗
Mixed-phase description of colossal magnetoresistive manganites
In view of recent experiments, indicating the spatial coexistence of conducting and insulating regions in the ferromagnetic metallic phase of doped manganites, we propose a refined mixed-phase description. The model is based on the competition of a double-exchange driven metallic component and a polaronic insulating component, whose volume fractions and carrier concentrations are determined self-consistently by requiring equal pressure and chemical potential. The resulting phase diagram as well as the order of the phase transition are in very good agreement with measured data. In addition, modelling the resistivity of the mixed, percolative phase by a random resistor network, we obtain a pronounced negative magnetoresistance in the vicinity of the Curie temperature $T_C$.
cond-mat.str-el↗
Interplay of charge, spin, orbital and lattice correlations in colossal magnetoresistance manganites
We derive a realistic microscopic model for doped colossal magnetoresistance manganites, which includes the dynamics of charge, spin, orbital and lattice degrees of freedom on a quantum mechanical level. The model respects the SU(2) spin symmetry and the full multiplet structure of the manganese ions within the cubic lattice. Concentrating on the hole doped domain ($0\le x\le 0.5$) we study the influence of the electron-lattice interaction on spin and orbital correlations by means of exact diagonalisation techniques. We find that the lattice can cause a considerable suppression of the coupling between spin and orbital degrees of freedom and show how changes in the magnetic correlations are reflected in dynamic phonon correlations. In addition, our calculation gives detailed insights into orbital correlations and demonstrates the possibility of complex orbital states.
cond-mat.str-el↗
Anderson localization of polaron states
Using the vanishing of the typical polaron tunneling rate as an indicator of the breakdown of itinerancy, we study the localization of polaron states in a generic model for a disordered polaronic material. We find that extremely small disorder causes an Anderson localization of small polaron states. However, the ratio between the critical disorder strength needed to localize all states in the polaron band and the renormalized bandwidth is not necessarily smaller than for a bare electron.
cond-mat.str-el↗