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arXiv:cond-mat/9804265 · Physical review. B, Condensed matter

Persistent current in a two-chain Hubbard model with impurities

弘之 森

Published Aug 15, 1998• 1 citation
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Abstract

The interplay between impurities and interactions is studied in the gapless phase in a two-chain Hubbard model in order to see how the screening of impurity potentials due to repulsive interactions in a single-chain model will be changed by increasing the number of channels. Renormalization-group calculations show that charge stiffness, and hence persistent current, of the two-chain model are less enhanced by interactions than in the single-chain case.

DOI
10.1103/physrevb.58.3486

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The interplay between impurities and interactions is studied in the gapless phase in a two-chain Hubbard model in order to see how the screening of impurity potentials due to repulsive interactions in a single-chain model will be changed by increasing the number of channels. Renormalization-group calculations show that charge stiffness, and hence persistent current, of the two-chain model are less enhanced by interactions than in the single-chain case.
The persistent current and charge stiffness of a one-dimensional Luttinger liquid on a ring threaded by a magnetic flux are calculated by Monte Carlo simulation. By changing the random impurity potential strength and the electron-electron interaction, we see a crossover behavior between weak- and strong-impurity limits. For weak-impurity potentials, interactions enhance impurity effects, that is, interactions decrease the current and the stiffness. On the other hand, interactions tend to screen impurities when the impurity potential is strong. Temperature dependence of the persistent current and the charge stiffness shows a peak at a characteristic temperature, consistent with a recent single-impurity study.
We studied effects of random potentials and roles of electron-electron interactions in the gapless phase of coupled Hubbard chains, using a renormalization group technique. For noninteracting electrons, we obtained the localization length proportional to the number of chains, as already shown in the other approaches. For interacting electrons, the localization length is longer for stronger interactions, that is, the interactions counteract the random potentials. Accordingly, the localization length is not a simple linear function of the number of chains. This interaction effect is strongest when there is only a single chain. We also calculate the effects of interactions and random potentials on charge stiffness.
We consider a one-dimensional Hubbard model in the presence of disorder. We compute the charge stiffness for a mesoscopic ring as a function of the size L, which is a measure of the persistent currents. We find that for finite disorder the persistent currents of the system with repulsive interactions are larger than those of the system with attractive interactions. This counterintuitive result is due to the fact that local-density fluctuations are reduced in the presence of repulsive interactions.
We study the behaviour of a single impurity potential within a combined method of renormalization group and bosonization in two dimensions. For repulsive interactions the backscattering components of the impurity potential are enhanced with respect to the other angles. We estimate the corrections to the conductivity as a function of . For we obtain similar results as in the non-interacting case. At finite temperatures, we obtain results controlled by the interactions. Here we identify a range of temperatures in which the conductivity increases with the lowering of the temperature.
The persistent current in a lattice model of a one-dimensional interacting electron system is systematically studied using a complex version of the density-matrix renormalization group algorithm and the functional renormalization group method. We mainly focus on the situation where a single impurity is included in the ring penetrated by a magnetic flux. Due to the interplay of the electron-electron interaction and the impurity the persistent current in a system of N lattice sites vanishes faster than 1/N.1/N.1/N. Only for very large systems and large impurities our results are consistent with the Bosonization prediction obtained for an effective field theory. The results from the density-matrix renormalization group and the functional renormalization group agree well for interactions as large as half the bandwidth, even though as an approximation in the latter method the flow of the two-particle vertex is neglected. This confirms that the functional renormalization group method is a very powerful tool to investigate correlated electron systems. The method will become very useful for the theoretical description of the electronic properties of small conducting ring molecules.
Using a one-dimensional spin-orbital model as a typical example of quantum spin systems with richer symmetries, we study the effect of an isolated impurity on its low-energy dynamics in the gapless phase through bosonization and renormalization-group methods. In the case of internal impurities, depending on the symmetry, the boundary fixed points can be either an open chain with a residual spin or (and) orbital triplet left behind, or a periodic chain. However, these two fixed points are indistinguishable in the sense that in both cases, the lead-correction-to-scaling boundary operators (LCBO) only show Fermi-liquid-like corrections to thermodynamical quantities (except the possible Curie-like contributions from the residual moments in the former cases). In the case of external (Kondo) impurities, the boundary fixed points, depending on the sign of orbital couplings, can be either an open chain with an isolated orbital doublet due to Kondo screening or an intermediate fixed point with the same LCBO as that of the two-channel Kondo problem. Comparison with the Kondo effect in one-dimensional Heisenberg spin chain and multiband Hubbard models is also made.