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arXiv:cond-mat/0311202 · Journal of the Physical Society of Japan

Dielectric Response of Interacting 1D Spinless Fermions with Disorder

Masato Kishi, Yasuhiro Hatsugai

Published Feb 15, 2004• 0 citations
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Abstract

Dielectric responces of the one-dimentional electron system is investigated numerically. We treat an interacting one-dimentional spinless fermion model with disorder by using the Density Matrix Renormalization Group(DMRG) method which is extended for nonuniform systems. We apply an electric field $E$ to the system and calculate dielectric responces. Dielectric responce of the Mott insulator and the Anderson insulator are calculated respectively. Steplike behaviors in $P-E$ curve are obtained which corresponds to breakdown of the insulating behavior. For the Mott insulator, the steps originate from generation of kink-pairs. For the Anderson insulator on the other hand, the origin of the steps is a crossing of the localized one particle energy levels. We also treat random systems with interaction. From one parameter scaling analysis of the susceptibility $χ$, the metal-insulator transition in attractively interacting region is confirmed and a phase diagram of the random spinless fermion model is obtained.

DOI
10.1143/jpsj.73.311

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We study the entanglement entropy(EE) of disordered one-dimensional spinless fermions with attractive interactions. With intensive numerical calculation of the EE using the density matrix renormalization group method, we find clear signatures of the transition between the localized and delocalized phase. In the delocalized phase, the fluctuations of the EE becomes minimum and independent of the system size. Meanwhile the EE's logarithmic scaling behavior is found to recover to that of a clean system. We present a general scheme of finite size scaling of the EE at the critical regime of the Anderson transition, from which we extract the critical parameters of the transition with good accuracy, including the critical exponent, critical point and a power-law divergent localization length.
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The interplay between Anderson localization and Mott localization is considered in the vicinity of one dimension for a collection of interacting spinless fermions or repulsive bosons. We demonstrate that in the absence of commensurability effects an Anderson localization transition does take place for d\ensuremath{\le}1. It is characterized by a critical dynamical exponent z having value z=2-d for d\ensuremath{\rightarrow}1-0, in disagreement with the previous claims that z always equals d. We find that there is only a localized phase for d>1 and expect that this similarity between free fermions and interacting quantum particles will be valid up to two dimensions. We also consider the competition between the effects of commensurability, disorder, and interaction in exactly one dimension. The outcome strongly depends on the order of umklapp scattering responsible for the formation of the Mott insulator in the pure case. If it is \ensuremath{\Delta}k=2kF{\mathit{k}}_{\mathit{F}}kF​ scattering and the disorder is sufficiently weak, the Mott phase survives and the Anderson phase intervenes almost everywhere between the Mott insulator and the conductor, except at one special symmetry-enhanced point corresponding to the fixed commensurate filling: here, as in the pure case, the Mott transition belongs to the Kosterlitz-Thouless universality class. For sufficiently strong disorder, or for any disorder and higher-order scattering, the path from the Mott insulator phase (if it survives) to the conductor always crosses the Anderson phase.
Using the density matrix renormalization group algorithm, we investigate the lattice model for spinless fermions in one dimension in the presence of a strong interaction and disorder. The phase sensitivity of the ground state energy is determined with high accuracy for systems up to a size of 60 lattice constants. This quantity is found to be log normally distributed. The fluctuations grow algebraically with system size with a universal exponent of $\ensuremath{\approx}2/3$ in the localized region of the phase diagram. Surprisingly we find, for an attractive interaction, a delocalized phase of finite extension. The boundary of this delocalized phase is determined.