Bulletin of the American Physical Society
APS March Meeting 2011
Volume 56, Number 1
Monday–Friday, March 21–25, 2011; Dallas, Texas
Session A24: Computational Methods I: Numerical Methods for Strongly Correlated Systems |
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Sponsoring Units: DCOMP Chair: Adrian Feiguin, University of Wyoming Room: D167 |
Monday, March 21, 2011 8:00AM - 8:12AM |
A24.00001: Modeling pump-probe spectroscopy in systems with electron-phonon coupling Alexander F. Kemper, Brian Moritz, Thomas P. Devereaux In pump-probe experiments, the electronic system is driven out of equilibrium by the application of a strong electric field. Phonons are of critical importance in returning the system to its original state, as they dissipate the energy introduced by the field. Using the non-equilibrium Keldysh formalism, we study how phonons affect the electronic current and energy in the Migdal limit, for both pulsed and continuous fields, and how this affects various spectroscopic measurements. Finally, we consider charge density- wave systems and their behavior in pump-probe experiments. [Preview Abstract] |
Monday, March 21, 2011 8:12AM - 8:24AM |
A24.00002: Pulsed-field pump-probe response in correlated systems B. Moritz, T.P. Devereaux, J.K. Freericks We describe pump-probe dynamics of the spinless Falicov-Kimball model subject to strong pulsed driving fields. The photoemission response shows a rapid evolution toward a new steady-state following decay of the pump pulse. We characterize the behavior by analyzing the power delivered to the system by the driving field and the corresponding change in the total energy. This prescription allows us to fit the result to an equilibrium response at a higher temperature determined self-consistently. For strong driving fields and correlations on the metallic side of the metal-insulator transition, the response can be described well by that of a system at a higher temperature; however, for correlations on the insulating side of the transition, the response in the nonequilibrium steady-state deviates significantly from that anticipated in quasi-thermal equilibrium. [Preview Abstract] |
Monday, March 21, 2011 8:24AM - 8:36AM |
A24.00003: Numerical study of interacting systems driven by a constant electric field Janez Bonca, Lev Vidmar, Marcin Mierzejewski, Peter Prelovsek, Stuart Trugman I will present a fundamental study of a Holstein polaron in one dimension and a single hole in the two dimensional t-J model driven away from the equilibrium by a constant electric field. Taking fully into account quantum effects we follow the time-evolution of systems from their ground state as the constant electric field is switched on at t=0, until they reach a steady state. At small electron phonon coupling (EP) the Holstein polaron experiences damped Bloch oscillations (BO) characteristic for a free electron band. An analytic expression of the steady state current is proposed in terms of EP coupling and electric field. We as well analyze the shape of the phonon tail that forms behind the traveling polaron. In the case of the t-J model we demonstrate that there exist three distinct regimes of the electric field (adiabatic, dissipative and the BO regime) which differ with respect to the real-time response. The d.c. current is shown to be maximal for a finite value of the electric field. [Preview Abstract] |
Monday, March 21, 2011 8:36AM - 8:48AM |
A24.00004: Dependence of Condensate Formation in Graphene Bilayers on Relative Layer Orientation Xuehao Mou, Dipanjan Basu, Leonard Register, Sanjay Banerjee It has been recently predicted that condensates can form between paired n-type and p-type graphene layers separated by a dielectric at room temperature under certain conditions. Recent works by the authors have explored the dependence of the condensate on dielectric thickness, dielectric constant, and charge densities including charge imbalance. However, to date only adjacent layers with the same crystal orientation have been modeled, such that the Dirac cones in each layer are precisely aligned with each other. In practice, obtaining such orientational alignment across a thin dielectric may be problematic. Therefore, the design of experiments to either prove or disprove the theory, and of devices to exploit this room temperature condensation should it exist, may depend critically on orientation dependence. In this work, we will theoretically consider the effects of crystal rotation on the existence and strength of the condensate using mean-field theory much as in the original works on the subject. [Preview Abstract] |
Monday, March 21, 2011 8:48AM - 9:00AM |
A24.00005: Self-consistent implementation of the multi-band Gutzwiller variational method: Formalism and combination with DFT Nicola Lanata', Hugo Strand, Xi Dai, Bo Hellsing We have generalized the approach for solving the multi-band Gutzwiller variational problem with density-density interaction to an arbitrary local interaction. The main advantage of our formulation is that it allows for a self-consistent numerical implementation which doesn't require any additional computational effort as compared to the simpler case of density-density interaction. Combined with DFT and the Local Density Approximation (LDA+Gutzwiller) our method allows for ab-initio study of multi-band correlated materials with full (rotationally invariant) Hund's rule coupling. We briefly introduce the method and present applications to several systems of correlated electrons. [Preview Abstract] |
Monday, March 21, 2011 9:00AM - 9:12AM |
A24.00006: Hole dynamics in a 2D doped quantum antiferromagnet within the non-crossing approximation Satyaki Kar, Efstratios Manousakis We study the doping evolution of the hole and magnon spectral functions of the two-dimensional $t-J$ and $t-t'-t''-J$ models by solving the Dyson's equations self-consistently within the non-crossing approximation. The doping dependence of the staggered magnetization and the hole spectral function are calculated for doping concentration where there is antiferromagnetic order for both of these models. We find that the intensity plot of the hole spectral function has characteristics similar to the ``waterfall'' features observed in the underdoped cuprates by ARPES. [Preview Abstract] |
Monday, March 21, 2011 9:12AM - 9:24AM |
A24.00007: Exact quantum dynamics of spin systems using the positive-P representation Ray Ng, Erik Sorensen We discuss a scheme for simulating the exact real time quantum dynamics of interacting quantum spin systems within the positive-P formalism. As model systems we study the transverse field Ising model as well as the Heisenberg model undergoing a quench away from the classical ferromagnetic ordered state. In using the positive-P representation (PPR), the dynamics of the interacting quantum spin system is mapped onto a set of stochastic differential equations (SDEs). The number of which scales linearly with the number of spins, N, compared to an exact solution through diagonalization that in the case of the Heisenberg model would require matrices exponentially large in N. This mapping is exact and can in principle be extended to higher dimensional interacting systems as well as to systems with an explicit coupling to the environment. We compare the results from using a PPR approach based on both the optical coherent states as well as SU(2) Radcliff coherent states. [Preview Abstract] |
Monday, March 21, 2011 9:24AM - 9:36AM |
A24.00008: Stochastic evaluation of Bold diagrammatic series for interacting Fermion problems: application to equilibrium and non-equilibrium quantum impurity models Emanuel Gull, David R. Reichman, Andrew J. Millis We present the first implementation of a bold expansion, i.e. a numerical sampling of the diagrammatic corrections to an analytic resummation. Our method is based on an expansion around the non-crossing approximation. The method is exact and applicable to both equilibrium and non-equilibrium problems. In equilibrium we show results for the single impurity Anderson model. In the non-equilibrium case we study an interacting quantum dot coupled to two leads and present results for current and occupation numbers for up to three times larger timescales than are reachable using a bare expansion. [Preview Abstract] |
Monday, March 21, 2011 9:36AM - 9:48AM |
A24.00009: Non-Local Corrections to the Dynamical Mean Field Theory for the Hubbard Model Herbert Fotso, Shuxiang Yang, Ka-Ming Tam, Juana Moreno, Mark Jarrell, Hartmut Hafermann We use the diagrammatic parquet formalism to calculate the non-local corrections to the Dynamical Mean Field Theory ($DMFT$) solution for the two-dimensional Hubbard model. The Dynamical Mean Field Theory vertex and Green's function are used as input to calculate the Feynman diagrams on a finite size cluster. This approach properly addresses the local as well as the short-range correlations, as illustrated by the agreement of the obtained local moment and the Neel critical temperature with Quantum Monte Carlo calculations on a $4$x$4$ cluster. [Preview Abstract] |
Monday, March 21, 2011 9:48AM - 10:00AM |
A24.00010: Regularization of Diagrammatic Series with Zero Convergence Radius Boris Svistunov, Lode Pollet, Nikolay Prokof'ev The divergence of perturbative expansions which occurs for the vast majority of macroscopic systems and follows from Dyson's collapse argument, prevents the direct use of Feynman's diagrammatic technique for controllable studies of strongly interacting systems. We show how the problem of divergence can be solved by replacing the original model with a convergent sequence of successive approximations which have a convergent perturbative series while maintaining the diagrammatic structure. As an instructive model, we consider the zero-dimensional $| \psi |^4$ theory. We believe that this approach opens up an opportunity to utilize Feynman's diagrams as a generic tool to address strongly correlated classical- and quantum-field systems, especially in the context of Diagrammatic Monte Carlo. [Preview Abstract] |
Monday, March 21, 2011 10:00AM - 10:12AM |
A24.00011: Discretization of the imaginary-time Greens function Andro Sabashvili, Mats Granath, Hugo Strand, Stellan Ostlund Finite temperature Greens functions are defined on an infinite set of Matsubara frequencies. A well known numerical difficulty is that the discontinuity in the Greens function in the imaginary time domain generates a long tail in the frequency representation which makes truncating a numerical calculation to to finite numbers of frequencies difficult. We have explored a particular ``periodization'' procedure designed to (1) close the Greens function approximation with a finite and relatively small number of Matsubara frequencies and (2) to be consistent with the Ward-Luttinger-Baym-Kadanoff variational principle. In addition to describing our truncation procedure we will show results of applying the method to standard DMFT calculations. We obtain results that are consistent with other well known but numerically more complex methods. [Preview Abstract] |
Monday, March 21, 2011 10:12AM - 10:24AM |
A24.00012: A general method for testing validity of one-particle spectral functions Jun Liu Based on the fact that the one-particle spectral function is uniquely extracted from a temperature Green function, a scheme is proposed to test the validity of a one-particle spectral function derived from any temperature Green function of any interacting system under thermal equilibrium. The physical implication of the scheme is discussed. An example is worked out to explicitly show the effectiveness of the scheme. [Preview Abstract] |
Monday, March 21, 2011 10:24AM - 10:36AM |
A24.00013: DMRG Study of the $S=1/2$ Kagome Antiferromagnetic Heisenberg Model Simeng Yan, Steven White, David Huse Recently we have completed a density matrix renormalization group (DMRG) study of the spin-$\frac{1}{2}$ Kagome antiferromagnetic Heisenberg model. We studied a variety of cylindrical geometries, with widths up to 12 lattice spacings and total sizes up to 400-500 sites. We found a spin liquid ground state with much lower energies than the valence bond crystal found using other approaches. Our energies are variational except for very tiny edge effects, and are comparable to Lanczos energies on 36 or 42 site. The spin liquid can be viewed as a melted valence bond crystal formed from 8 site diamond loops and dimers, with a 12 site unit cell, called the ``diamond pattern.'' In this talk we will focus on the narrowest cylinders, in particular a cylinder with a circumference of 4 lattice spacings which accomodates the diamond pattern, but for which the spin liquid ground state, while metastable in DMRG, is higher in energy than another state with a ``topological string'' and a resulting ``valence bond density wave'' broken translational symmetry. We discuss singlet and triplet gaps relative to these two states. The peculiar behavior of this narrow cylinder is presumably due to short resonance loops around the cylinder. [Preview Abstract] |
Monday, March 21, 2011 10:36AM - 10:48AM |
A24.00014: DMRG-optimized NRG treatment of sub-ohmic spin-boson model Cheng Guo, Andreas Weichselbaum, Matthias Vojta, Jan von Delft The sub-ohmic spin-boson model exhibits an interesting and much-studied quantum phase transition from a delocalized phase at weak spin-bath coupling to a localized phase at strong coupling. Previous works using NRG to calculate the critical exponents of this model near the phase transition failed partly because it cannot deal with the large number of states per bath oscillator required to describe the localized phase [1]. We show how this problem can be overcome by using DMRG to construct, for each site of the Wilson chain, an optimized boson basis containing only a small number of states, and using the resulting basis for standard NRG calculations. Our results are in good agreement with analytical predictions for this model. The approach presented here should be generalizable to other quantum impurity models with complex baths. \\[4pt] [1] M. Vojta, N.-H. Tong, R. Bulla, Quantum Phase Transitions in the Sub-Ohmic Spin-Boson Model: Failure of the Quantum-Classical Mapping, Phys. Rev. Lett. 94, 070604 (2005); Erratum: Phys. Rev. Lett., 102, 249904 (2009) [Preview Abstract] |
Monday, March 21, 2011 10:48AM - 11:00AM |
A24.00015: Resonant Inelastic X-ray Scattering in the Falicov-Kimball model Nandan Pakhira, James Freericks, Andrij Shvaika We calculate Resonant Inelastic X-ray Scattering (RIXS) spectra in the Falicov-Kimball model. Using Dynamical Mean Field Theory (DMFT) we do a detailed study of the RIXS response as a function of incident photon energy ($\omega_{in}$) or photon energy transfer ($\Omega$) for various photon momentums transfer ($\mathbf{q}$), temperature and other parameters of the model. We also calculate the dynamic structure factor, $S(\mathbf{q},\Omega)$, for this model and study its possible relation with the RIXS spectra. We find that for large incident photon energy (much larger than the resonant energy) the resonant contribution to RIXS spectra essentially vanishes and $S(\mathbf{q},\Omega)$ is proportional to the non-resonant part of the response. Finally, time permitting, we will also present Auger life time broadening effects on the RIXS spectra. [Preview Abstract] |
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