Bulletin of the American Physical Society
2006 APS March Meeting
Monday–Friday, March 13–17, 2006; Baltimore, MD
Session R27: Many-Body/Strongly Correlated |
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Sponsoring Units: DCOMP Chair: Gerardo Ortiz, Los Alamos National Laboratory Room: Baltimore Convention Center 324 |
Wednesday, March 15, 2006 2:30PM - 2:42PM |
R27.00001: Density Matrix Renormalization Group algorithm on intersecting chains Haihui Guo, Steven White Systems of intersecting chains are interesting both from a fundamental viewpoint and because of their potential use in nanoscale devices. Here, we will introduce a new density matrix renormalization group algorithm to perform calculations on intersecting chains systems. The new DMRG algorithm greatly reduces the number of states kept per block to roughly $\sqrt{m}$ compared with the alternative ``non-local'' approach. We present results on 3-chain Heisenberg $S=1$ system with two geometries, one with a single site in the center of junction, the other with three sites in the center of junction. [Preview Abstract] |
Wednesday, March 15, 2006 2:42PM - 2:54PM |
R27.00002: Finite-temperature density matrix renormalization using an enlarged Hilbert space Adrian E. Feiguin, Steven R. White We apply a generalization of the time-dependent DMRG to study finite temperature properties of several quantum spin chains, including the frustrated $J_1-J_2$ model. We discuss several practical issues with the method, including use of quantum numbers and finite size effects. We compare with transfer-matrix DMRG, finding that both methods produce excellent results. [Preview Abstract] |
Wednesday, March 15, 2006 2:54PM - 3:06PM |
R27.00003: DMRG meets NRG Andreas Weichselbaum, Frank Verstraete, Ulrich Schollw\"ock, J. Ignacio Cirac, Jan von Delft We present a unified framework of renormalization group methods, including Wilson's numerical renormalization group (NRG) and White's density-matrix renormalization group (DMRG), within the language of matrix product states. This allows to improve over Wilson's NRG for quantum impurity models by a variational method optimal in this framework. We illustrate it for the single-impurity Anderson model; moreover we use a variational method for evaluating Green's functions. The proposed method is more flexible in its description of off-resonance spectral properties, opening the way to time-dependent, out-of-equilibrium impurity problems. It also substantially improves computational efficiency for one-channel impurity problems, suggesting \emph{linear} scaling of complexity for $n$-channel problems. [Preview Abstract] |
Wednesday, March 15, 2006 3:06PM - 3:18PM |
R27.00004: Strong Coupling Polaron in 2D in Terms of the Bethe-Salpter Equation Russell Selva, Yuriy Malozovsky We consider the formation of polaron in two dimensions in terms of the Bethe-Salpeter equation. We develop the perturbation diagram approach to the electron-phonon interaction problem and show that the series of the ladder diagrams lead to the well-known Bethe-Salpeter equation. We evaluate the self-energy of the polaron. We show that even in the case of the weak electron-phonon interaction there at least one bound state exists for the polaron in two dimensions. We consider the formation of the polaron for the interaction of an electron both with acoustic and optical phonons. We have found the existence of the strong coupling polaron in both cases. [Preview Abstract] |
Wednesday, March 15, 2006 3:18PM - 3:30PM |
R27.00005: Collective fields in the functional RG for fermions: Vacuum expectation values and spontaneous symmetry breaking Florian Schuetz, Peter Kopietz We discuss partial bosonization of interacting electron systems by a Hubbard-Stratonovich transformation and derive the functional renormalization group equations for the one-line-irreducible vertices of the resulting coupled field theory containing fermionic and collective bosonic fields. We analyze different choices of the cutoff in either the fermionic or the bosonic propagator. Recently,we have shown that for the Tomonaga-Luttinger model a purely bosonic cutoff can be combined with Ward identities to solve a whole hierarchy of flow equations and to reproduce the exact solution for the single particle Green's function known from bosonization [1]. Here, we generalize our approach to include the possibility that some bosonic components of the field have a finite vacuum expectation value. The system of flow equations is then modified and supplemented by a flow equation for the vacuum expectation value of the field. For bosonic fields describing fluctuations in the zero-sound channel, the vacuum expectation value of the zero mode is closely related to the fermionic density, which can be exploited to calculate the compressibility. By using a cutoff in the free bosonic propagator, the renormalization group flow can be set up to systematically yield corrections to the self-consistent Hartree approximation. [1] F. Schuetz, L. Bartosch, and P. Kopietz, Phys. Rev. B 72, 035105 (2005) [Preview Abstract] |
Wednesday, March 15, 2006 3:30PM - 3:42PM |
R27.00006: Ab initio Anderson impurity approach to x-ray absorption spectra of transition metal complexes Daniel L. Cox, Arnd Hubsch, Montiago X. LaBute We present a generic Anderson impurity approach to transition metal molecules that allows to study correlation effects beyond the usual electronic structure calculations. Here, first principle density functional theory calculations (using SIESTA) are employed to determine the parameter of the model Anderson impurity Hamiltonian. We use the Lanczos algorithm to diagonalize the model Hamiltonian within a restricted set of basis states that is built up in the spirit of of the Gunnarsson Sch\"{o}nhammer trial wave function for heavy fermion compounds. The presented approach is applied to the K-edge x-ray absorption spectra of the valence tautomer molecule Co(3,5-DTBSQ)$_{2}$(phen). [Preview Abstract] |
Wednesday, March 15, 2006 3:42PM - 3:54PM |
R27.00007: Anomalous tunneling of bound pairs in crystal lattices Pavel Kornilovitch, Vladimir Bulatov A novel non-perturbative method of solving scattering problems for bound pairs on a lattice is developed. Two different break- ups of the Hamiltonian are employed to calculate the full Green operator and the wave function of the scattered pair. The calculation converges exponentially in the number of basis states used to represent the non-translationâ€“invariant part of the Green operator. The method is general and applicable to a variety of scattering and tunneling problems. As the first application, the problem of pair tunneling through a weak link on a one-dimensional lattice is solved. It is found that at the momentum values close to $\pi$ the pair tunnels much easier than one particle, with the transmission coefficient approaching unity. This anomalously high transmission is a consequence of the existence of a two-body resonant state localized at the weak link. [V.L. Bulatov and P.E. Kornilovitch, Europhys. Lett. {\bf 73}, 352 (2005).] [Preview Abstract] |
Wednesday, March 15, 2006 3:54PM - 4:06PM |
R27.00008: Non-Markovian dynamics on one-dimensional quantum lattices Michael Zwolak Recently ideas from Quantum Information have sparked a number of advances in the simulation of interacting quantum lattice systems. Vidal first proposed a method, dubbed the Time Evolving Block Decimation (TEBD) algorithm, to simulate real-time dynamics of pure states on one-dimensional lattices. [1] Subsequently this method was extended to the simulation of mixed states, including real-time dynamics governed by a Markovian master equation and construction of thermal states. [2] These methods scale linearly in the system size, enabling relatively large lattices to be studied. We present a more general extension of the TEBD algorithm which allows one to simulate non-Markovian master equations within the Born approximation. This method scales quadratically with the system size. We demonstrate the method with examples of spins and fermions. We also discuss applications to systems driven out of equilibrium by external reservoirs. [1] G. Vidal, Phys. Rev. Lett. 91, 147902 (2003); 93, 040502 (2004). [2] M. Zwolak, G. Vidal, Phys. Rev. Lett. 93, 207205 (2004). [Preview Abstract] |
Wednesday, March 15, 2006 4:06PM - 4:18PM |
R27.00009: Exotic excitations with fractional charges on frustrated lattices Erich Runge, Frank Pollmann, Peter Fulde Geometrical frustration of lattices can lead to a macroscopic degeneracy in the classical limit and thus to many interesting physical effects. In spin systems these are e.g. translational invariant spin liquid ground states and deconfined spinons. In contrast to magnetic properties, one began only recently to explore the charge degrees of freedom on frustrated lattices. For the systematic study of charge degrees of freedom, we consider a model of spinless Fermions with nearest-neighbor hopping $t$ and Coulomb repulsion $V$. Quantum fluctuations reduce the classical ($t=0$) macroscopic degeneracy. For the strongly correlated limit $V\gg|t|$, it has been predicted that an added electron can decay into two mobile quasi-particles, leading to fractional charges of $e/2$ in 2D and 3D systems. For a deeper understanding of these charge degrees of freedom we calculated numerically the properties of static and dynamic charges on the 2D checkerboard lattice. We find evidence for a weak confinement between two fractional charges leading to excitations with very large spatial extend. Furthermore, we argue that the fractional charges are probably deconfined on the 3D pyrochlore lattice. [Preview Abstract] |
Wednesday, March 15, 2006 4:18PM - 4:30PM |
R27.00010: Making an analogy between a multi-chain interaction in Charge Density Wave transport and the use of wave functionals to form S-S' pairs. Andrew Beckwith First, we show through a numerical simulation that the massive Schwinger model used to formulate solutions to CDW transport in itself is insufficient for transport of soliton-antisoliton (S-S') pairs through a pinning gap model of CDW transport. We show that a model Hamiltonian with Peierls condensation energy used to couple adjacent chains (or transverse wave vectors) permits formation of S-S' pairs which could be used to transport CDW through a potential barrier .Previously, we have argued that there are analogies between this construction and the false vacuum hypothesis used for showing a necessary and sufficient condition for formation of CDW S-S' pairs in wavefunctionals. Here we note that this can be established via either use of the Bogomil'nyi inequality or an experimental artifact which is due to use of the false vacuum hypothesis to obtain a proportional `distance' between the S-S' charge centers. [Preview Abstract] |
Wednesday, March 15, 2006 4:30PM - 4:42PM |
R27.00011: Localized component method for few-body scattering and bound state calculations Vladimir Roudnev A modification of Faddeev equations which admits a very effective computational scheme is proposed. The method allows to perform precise calculations of bound states and scattering in few-body systems. For the systems having loosely bound subsystems the method can reduce the computation time by an order of magnitude. We illustrate the method by calculating bound states and scattering of three atoms with a simple model interaction. We also report results for systems of noble gas atoms with realistic interactions. [Preview Abstract] |
Wednesday, March 15, 2006 4:42PM - 4:54PM |
R27.00012: Equilibrium technique applied to strongly correlated electron transport in steady-state nonequilibrium Jong Han We present a quantum algorithm of nonequilibrium steady-state transport within the equilibrium formalism. Current-carrying nonequilibrium ensemble is constructed by the Boltzmann factor $\exp[-\beta(\hat{H}-\hat{Y})]$ using the bias operator $\hat{Y}$ which imposes the boundary condition of different chemical potentials in source-drain reservoirs of electronic device. In the limit of non-interacting quantum dot systems, the mapping of a nonequilibrium to an effective equilibrium system can be explicitly shown to reproduce the Landauer-B\"uttiker formula. The equilibrium formulation is successfully applied to the strongly correlated transport of the Kondo regime, with the anomalous Kondo peak at small voltage bias and incoherent inelastic transport at high bias. This demonstrates that the numerical tools developed in equilibrium theory, such as quantum Monte Carlo, exact diagonalization, or renormalization group methods, can be applied in nonequilibrium and complement the existing theories based on nonequilibrium Greens function technique. [Preview Abstract] |
Wednesday, March 15, 2006 4:54PM - 5:06PM |
R27.00013: Cluster Impurity Solver for LDA+DMFT Calculations Quan Yin, Sergey Savrasov We report the electronic structure calculations of strongly correlated systems such as Mott Insulators, using the LDA+DMFT method. LDA+DMFT is a combination of the Density Functional Theory and the Dynamical Mean Field Theory featuring both the one-electron approximation and the many-body treatment for electrons, which is suitable for any ratio of coulomb repulsion over band width, and all computations are self-consistent. In the process of solving the Anderson Impurity Model for DMFT, several solvers with different accuracy were used and their results are compared. This presentation will focus on our most recently developed cluster solver and its applications. [Preview Abstract] |
Wednesday, March 15, 2006 5:06PM - 5:18PM |
R27.00014: Many-body Co-tunneling in Coupled Quantum Dots Carolyn Young, Michael Hilke We developed a new formalism which allows us to study co-tunneling events in coupled quantum dot structures. By generalizing the non-equilibrium Green's function (NEGF) method for the case of N-particle Green's functions, we are able to calculate the many-body self-energy associated with semi-infinite leads. This formalism can be used to calculate the co-tunneling contribution to the differential conductance of various structures, such as parallel- and serial-coupled quantum dots, as well as Aharonov-Bohm interference devices. [Preview Abstract] |
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