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We calculate the photoemission spectral function of the one-dimensional Hubbard model away from half filling using the dynamical density matrix renormalization group method. An approach for calculating momentum-dependent quantities in finite open chains is presented. Comparison with exact Bethe Ansatz results demonstrates the unprecedented accuracy of our method. Our results show that the photoemission spectrum of the quasi-one-dimensional conductor TTF-TCNQ provides evidence for spin-charge separation on the scale of the conduction band width.
Full quantum calculations on nanoscale devices are most often unfeasible due to the exponentially large Hilbert space of such models. Approximate methods going beyond perturbation theory and mean-field calculations are therefore of great interest when studying such systems. The Density Matrix Renormalization Group (DMRG) [1, 2] is one such method capable of giving very accurate results, and applicable to very many different systems. We follow the work of Berkovits [3] and implement standard DMRG on a quantum dot coupled to a single semi-infinite lead, and use this implementation to calculate the occupation of the dot for various model parameters [4]. We generalize the implementation to treat also two leads and report results. In the non-interacting limit we calculate analytically the occupation of the dot using Green's function theory. Keeping sufficiently many states in the DMRG calculation we find good consistency between DMRG and analytic results.
[1] S.R. White, PRL 69, 2863 (1992).
[2] S.R. White, PRB 48, 10345 (1993).
[3] R. Berkovits, cond-mat/0306284 (2003).
[4] D. Bohr, M.Sc. Thesis (2004), available at
www.mic.dtu.dk/research/TheoreticalNano/images/DanBohr_MScThesis.pdf.
V.O.Cheranovskii, A.A.Chovpan, E.V.Ezerskaya, and I.Özkan
We studied the energy spectrum and low-temperature thermodynamics of two-leg spin-1/2 ladder model with anisotropic coupling. For the model with XY interaction along the legs we found the exact energy spectrum of the states with two inverted spins and conditions for the existence of corresponding bound states. The latter do not exist in the case of isotropic coupling in rungs. We also performed the DMRG study of the lowest energy states of the infinite lattice for several numbers of inverted spins, and found that the bound states with three inverted spins exist at least for some regions of model parameters. On the basis of this study we proposed a simple approximate formula for the specific heat of a ladder with strongly interacting rungs. The results of direct diagonalization study of temperature dependence of heat capacity for finite lattice clusters agree well with our approximation. We found that this dependence may have up to three maxima in zero magnetic field. It is also shown, that in strong ferromagnetic coupling limit the lower-energy states of anisotropic spin ladder are described by XXZ spin-1 chain with single ion anisotropy.
The Luttinger-liquid parameter $K_\rho$ is a very important quantity to know properties of a low-dimensional metallic system, however, it is not easy to obtain $K_\rho$ precisely except for the one-dimensional (1D) ordinary Hubbard model. We show an estimation of $K_\rho$ from the slope of density-density correlation function $N(q)$ as $q\rightarrow 0^+$ with open boundary conditions, using the density-matrix renormalization group (DMRG) method. We find excellent agreement between DMRG results and exact ones for all fillings $n$ and interaction strengths $U$ in the 1D Hubbard model. Moreover, we introduce the long-range Coulomb interactions and discuss the behavior of $K_\rho$ in the vicinity of charge-density-wave instabilities at several commensurate fillings.
G. Hager, E. Jeckelmann, H. Fehske and G. Wellein
We present two different approaches by which shared-memory parallelization of the standard DMRG algorithm can be accomplished in an efficient way. The parallelized code shows good scalability up to at least eight processors and allows us to solve problems which exceed the capability of sequential DMRG calculations[1]. As an example, we investigate the formation of stripes in 6-leg Hubbard ladders doped away from half filling. Our parallelized code allows us to study large systems with up to 28x6 sites while keeping up to 8000 density-matrix eigenstates per block on contemporary SMP systems.
[1] G. Hager, E. Jeckelmann, H.Fehske, and G. Wellein, J. Comp. Phys. 194, pp. 795-808 (2004).
The coupled cluster method is one of the most successful methods in the fields on finite systems such as quantum chemistry. However, we are often restricted to use up to the double excitation operator with respect to the Hartree-Fock vacuum in the practical applications because of huge computational requirements to manipulate higher order cluster operators. This restriction prevent us from obtaining the level of accuracy required. We will present how to avoid that bottleneck using an idea related with the DMRG and numerical results on several molecules.
J. Rissler, R. M. Noack, S. R. White
The ordering of sites in systems with long-range interaction plays an important role for the convergence of the DMRG algorithm. An example for this is the QCDMRG where the sites are molecular orbitals and the stationary, non-relativistic Schrödinger equation in the clamped-nuclei approximation is investigated (Full Configuration-Interaction). Due to the success of DMRG in problems with local interaction, the idea is to localise the interaction between the molecular orbitals along the DMRG chain. Based on a two-site density matrix, a measure for orbital-orbital interaction is determined and different localisation schemes are tested and compared with other methods in the literature.
Masaki Tezuka, Ryotaro Arita and Hideo Aoki
We have applied the pseudo-site method[1] for the Holstein-Hubbard model, one of the simplest models that have both electron-electron and electron-phonon interactions. While the pseudo-site method starts to be applied to correlated systems[2], we have noticed that important states tend to be discarded at the stage of infinite algorithm, where the electrons experience the bare Hubbard $U$ at the central site before the phonon pseudo-sites are added. To amend this we have developed a new technique, where the value of $U$ at the added electron pseudo-site is modified in such a way that the expectation number of electrons at the site is close to the average band filling when we calculate the ground state for the superblock. We show that this indeed improves the convergence at least for half-filled bands, and present the results for the charge, spin and pair correlation functions in the region where the phonon-mediated attractive interaction is comparable to $U$ in magnitude. We also discuss the possibility of applying the technique to other systems having internal degrees of freedom.
[1] E. Jeckelmann and S.R. White, Phys. Rev. B 57, 6376 (1998).
[2] H. Fehske, G. Wellein, G. Hager, A. Weisse and A.R. Bishop, Phys. Rev. B 69, 1651
15 (2004).