No abstract

We study the Drude weight, optical conductivity, and flux-periodicity properties of one-dimensional Hubbard chains using Bethe-ansatz, Lanczos, and exact-diagonalization techniques. We find that the Drude weight D is unexpectedly negative for half-filled Hubbard rings with N =4n sites rejecting a strong paramagnetic response, while it is positive (diamagnetic) for half-filled rings of N =4n +2 sites.In both cases at half filling, D vanishes exponentially with N on a length scale set by the inverse of the gap for small U/t. Near half filling, we find that D approaches a constant, positive, diamagnetic value as N increases, indicating metallic behavior. Combining Bethe-ansatz results near half filling with the known U =0 and U = ao limits and Lanczos finite-size extrapolations, we obtain a general picture of D in the thermodynamic limit as a function of band filling and the ratio U/t. We note similarities with the low-frequency integrated spectral weight of certain hole-doped and electron-doped high-T, compounds.We investigate the finite-frequency optical conductivity, finding structure at co= U and, for one hole off half filling, at co~t /U. We find that minima in the energy of a Hubbard ring enclosing a Aux N occur with changes of half a Aux quantum rather than a full Aux quantum when the Coulomb repulsion is turned on. Lastly, we discuss the relationship of the Drude weight computed from open chains to that obtained from rings, and also the effect of arbitrary phases at the ring boundary.

Local denaturation, the separation at specific sites of the two strands comprising the DNA double helix, is one of the most fundamental processes in biology, required to allow the base sequence to be read both in DNA transcription and in replication. In living organisms this process can be mediated by enzymes which regulate the amount of superhelical stress imposed on the DNA. We present a numerically exact technique for analyzing a model of denaturation in superhelically stressed DNA. This approach is capable of predicting the locations and extents of transition in circular superhelical DNA molecules of kilobase lengths and specified base pair sequences. It can also be used for closed loops of DNA which are typically found in vivo to be kilobases long. The analytic method consists of an integration over the DNA twist degrees of freedom followed by the introduction of auxiliary variables to decouple the remaining degrees of freedom, which allows the use of the transfer matrix method.

We investigate the magnetic properties of the Kondo two-impurity Hamiltonian with a recently introduced, essentially exact quantum Monte Carlo technique. We explore in particular the competition between Kondo effect, with Kondo temperature T&, and Ruderman-Kittel-Kasuya-Yosida (RKKY) interactions, with coupling constant d. We simulate the regimes~d~& Tr and~d~& Ts for both ferromagnetic and antiferromagnetic cf, considering in particular the antiferromagnetic regime 8/Tz =2.4 where anomalous behavior is predicted from renormalization-group calculations.Over the entire parameter range, we find that nearby impurity spin-spin correlations initially develop according to a RKKY effective Hamiltonian H, &=PS&.S, as the temperature is lowered; the correlations then saturate at around the Kondo temperature Tz. This result suggests an analogous picture for the lattice case, with long-range order developing if a "RKKY lattice" transition ternperature is reached before Kondo quenching effects set in. We also find no evidence for anomalous staggered susceptibility behavior in the 8/T& =2.4 regime, and give possible explanations for this difference with the renormalization-group results.dom would then be quenched at two new Kondo temperatures, with spin 1~spin--, quenching followed by spin -, '~spin 0, through conduction electron channels even and odd around the midpoint of the two impurities.Quantum Monte Carlo studies were done on the twoimpurity Anderson system, for the ferromagnetic casẽ d~~T tc and the antiferromagnetic case ot ((Tt;. It was found that spin correlations developed according to a RKKY elFective Hamiltonian (H,s. =PS, . S2) approximately down to the Kondo temperature, at which point they ceased further development. One can picture this qualitatively as Kondo spin fIuctuations beginning to dominate thermal spin Auctuations around the Kondo temperature; then, regarding impurity spin correlations, the system would be effectively at temperature T~f or all 40 4780 1989 The American Physical Society 40 QUANTUM MONTE CARLO STUDY OF THE TWO-IMPURITY. . . 4781T (T~. If the RKKY coupling was ferromagnetic, the normalized uniform susceptibility was enhanced and the staggered susceptibility the same as, or slightly deenhanced, when compared to single-impurity susceptibility values. Because of the small 4/Tz ratio, the trend was dificult to distinguish for antiferromagnetic RKKY coupling. However, in that case, the staggered susceptibility appeared slightly enhanced over the uniform susceptibility.In addition to extending the parameter regime studied, one of the purposes of this paper is to examine to what extent these findings for the Anderson model are affected by charge fluctuations. Thus, we study here mainly the Kondo Hamiltonian of Eq. (1), where charge fluctuations are eliminated at the outset. (Some new results for the Anderson Hamiltonian are also presented. ) This also allows a more direct comparison with recent renormalization-group and auxiliary boson studies of the twoimpurity Kondo Hamiltonian.The renormal...

No abstract