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Journal of the Physical Society of Japan

Quantum Monte Carlo Study on Impurity Pinning in One-Dimensional Interacting Electron Systems–Competition between Charge Density and Superconducting Fluctuations–

Tetsuro Saso, Yoshikazu Suzumura

Published Sep 15, 1986• 2 citations
Publisher

Abstract

Effects of random impurities on one-dimensional interacting electron systems are studied by use of the quantum Monte Carlo method and the phase variable representation of charge density and superconducting fluctuations. The impurities pin the phase variable of charge density fluctuation, whereas the quantum fluctuation around the pinned state reduces the pinning effect yielding increase of the superconducting fluctuation since the charge density and the superconducting fluctuations are complementary to each other. Such interplay between randomness and interactions is shown explicitly by calculating spatial dependence of quantum fluctuations, metastable states and correlation functions for superconductivity. Quantum character of metastable states is discussed. It is found that superconducting state is more sensitive to impurities than charge density wave state when the interaction between electrons is weak.

DOI
10.1143/jpsj.55.3151

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We investigate the effects of the randomness and electron-electron interactions on the competition between superconductivity and charge density wave in one-dimensional bipolaron system in the half-filled case at finite temperatures. The model is transformed into the S =1/2 XXZ-chain with random fields, and we carry out the numerical simulation using the transfer matrix by Suzuki-Trotter formula. When the interaction between neighboring bipolarons is attractive, the suppression of the correlation functions is described by the scaling law. This result is discussed in connection with the Fukuyama-Lee length including the quantum fluctuations. When the interaction is repulsive, weak randomness suppresses the charge density wave and enhances the superconductivity, but strong randomness suppresses both.
In this paper, recent theoretical developments on Anderson localization in one-dimensional electron systems are reviewed. First, the theories for noninteracting systems are summarized together with the various results based on numerical simulation. Special attention will be paid to the dynamical structure of the systems. The second part discussed Anderson localization in interacting electron systems by the phase Hamiltonian, and the close relationship between the localization and the impurity pinning of charge density wave is demonstrated. Results of the numerical simulations by quantum Monte Carlo technique are also presented.
Abstract The interplay between quantum and thermal fluctuations in the presence of quenched random disorder is a long-standing open theoretical problem which has been made more urgent by advances in modern experimental techniques. The fragility of charge density wave order to impurities makes this problem of particular interest in understanding a host of real materials, including the cuprate high-temperature superconductors. To address this question, we consider the quantum version of an exactly solvable classical model of two-dimensional randomly pinned incommensurate charge density waves first introduced by us in a recent work, and use the large-N technique to obtain the phase diagram and order parameter correlations. Our theory considers quantum and thermal fluctuations and disorder on equal footing by accounting for all effects non-perturbatively, which reveals a novel crossover between under-damped and over-damped dynamics of the fluctuations of the charge density wave order parameter.
The properties of nanoscopic rings with electronic correlations and impurities are analyzed numerically by means of two methods. First, we carry out exact diagonalization of one-dimensional rings that consist of up to several lattice sites. Then, we perform the Bogoliubov--de Gennes equation studies of finite-width rings consisting of a few hundred sites. Results obtained from both approaches are shown to be consistent. We demonstrate how the system properties are affected by various configurations of impurities for both repulsive and attractive electron--electron interactions. In the case of attractive interaction we show that the nanoscopic properties are mainly determined by the competition between tendencies toward pairing and formation of the density waves. Since the impurities act as pinning centers for the density waves, their configuration determines the result of this competition.
The interplay between electron-electron correlations and disorder has been a central theme of condensed matter physics over the past several decades, with particular interest in the possibility that interactions might cause delocalization of an Anderson insulator into a metallic state, and the disrupting effects of randomness on magnetic order and the Mott phase. Here we extend this physics to explore electron-phonon interactions and show, via exact quantum Monte Carlo simulations, that the suppression of the charge density wave correlations in the half-filled Holstein model by disorder can stabilize a superconducting phase. Our simulations thus capture qualitatively the suppression of charge ordered phases and emergent superconductivity recently seen experimentally.