Bulletin of the American Physical Society
APS March Meeting 2014
Volume 59, Number 1
Monday–Friday, March 3–7, 2014; Denver, Colorado
Session W27: Quantum Many-Body Systems II |
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Sponsoring Units: DCOMP Chair: Aldo Romero, West Virginia University Room: 501 |
Thursday, March 6, 2014 2:30PM - 2:42PM |
W27.00001: Generalized Cumulant Expansion for the One Electron Green's Function J.J. Kas, J.J. Rehr, L. Reining The cumulant expansion has proved extremely useful in describing many-body excitations. For example, the approach rectifies the failure of the GW approximation to account for multiple satellites in x-ray photoemission spectra.\footnote{Matteo Guzzo, Giovanna Lani, Francesco Sottile, Pina Romaniello, Matteo Gatti, Joshua J. Kas, John J. Rehr, Mathieu G. Silly, Fausto Sirotti, and Lucia Reining, Phys. Rev. Lett. 107, 166401 (2011)} However, current implementations are inadequate since they ignore diagrams that lead to partial occupations and satellite features in the spectral function both above and below the Fermi surface. Here, we correct these limitations using a cumulant expansion of the retarded one-electron Green's function. At 2nd order in the effective boson couplings, the cumulant is proportional to the GW self-energy. Thus the cumulant method extends the GW Green's function without additional computational expense, and can therefore be used for complex systems. We test the approach on the homogeneous electron gas, and present results for a range of parameters that are physically relevant for condensed matter systems. The resulting spectral function is used for calculations of occupation numbers, quasiparticle properties, and correlation energies. [Preview Abstract] |
Thursday, March 6, 2014 2:42PM - 2:54PM |
W27.00002: Solid-state calculations using the second-order M{\o}ller-Plesset perturbation theory combined with the transcorrelated method Masayuki Ochi, Shinji Tsuneyuki Recently, wave-function theory has been actively applied to solid-state calculations, where the Hartree-Fock (HF) method is used as a starting point. Transcorrelated (TC) method [1-5] is expected to be an attractive alternative to the HF method, in which the total wave function is assumed to be the Jastrow-Slater-type wave function, and the many-body Hamiltonian is similarity-transformed by the Jastrow factor. Then the electron correlation effects are taken into account through the similarity-transformed Hamiltonian. However, the band gaps calculated using the TC method have about 1 or 2 eV errors for some semiconductors. For improving accuracy, we apply the second-order M{\o}ller-Plesset (MP2) perturbation theory to the similarity-transformed Hamiltonian, and will show that the band structures of solids are corrected well with the same level of computational cost as that for conventional MP2 applied to the HF method.\\[4pt] [1] S. F. Boys and N. C. Handy, Proc. R. Soc. London Ser. A 309, 209 (1969).\\[0pt] [2] S. Ten-no, Chem. Phys. Lett. 330, 169 (2000).\\[0pt] [3] N. Umezawa and S. Tsuneyuki, J. Chem. Phys. 119, 10015 (2003).\\[0pt] [4] R. Sakuma and S. Tsuneyuki, J. Phys. Soc. Jpn. 75, 103705 (2006).\\[0pt] [5] M. Ochi, K. Sodeyama, R. Sakuma, and S. Tsuneyuki, J. Chem. Phys. 136, 094108 (2012). [Preview Abstract] |
Thursday, March 6, 2014 2:54PM - 3:06PM |
W27.00003: Statistical mechanics of Coulomb gases as quantum theory on Riemann surfaces Tobias Gulden, Michael Janas, Alex Kamenev Statistical mechanics of 1D Coulomb gases may be mapped onto (in general) non-Hermitian quantum mechanics. We use this example to develop non-Hermitian instanton calculus. Treating momentum and coordinate as independent complex variables, constant energy manifolds are given by Riemann surfaces of genus $g\geq1$. The actions along principal cycles on these surfaces obey an ODE in the moduli space of the Riemann surface known as the Picard-Fuchs equation. Solving the Picard-Fuchs equation yields semiclassical spectra as well as instanton effects such as width of Bloch bands (the latter determines energy barrier for charge transport). Both are shown to be in perfect agreement with numerical simulations. Applications include transport through biological ion channels as well as nanofluidics, e.g water filled nanotubes. [Preview Abstract] |
Thursday, March 6, 2014 3:06PM - 3:18PM |
W27.00004: Off-Center Thawed Gaussian Multi-Dimensional Approximation for Semiclassical Propagation Lucas Kocia, Eric Heller The Off-Center Thawed Gaussian Approximation's (OCTGA) performance in multi-dimensional coupled systems is shown in comparison to Herman-Kluk (HK), the current workhorse of semiclassical propagation in the field. As with the Heller-Huber method and Van Voorhis \emph{et~al.}'s nearly-real method of trajectories, OCTGA requires only a single trajectory and associated stability matrix at every timestep to compute Gaussian wave packet overlaps under any Hamiltonian. This is in sharp contrast to HK which suffers from the necessity of having to propagate thousands or more computationally expensive stability matrices at every timestep. Unlike similar methods, the OCTGA relies upon a single \emph{real} guiding trajectory, which in general does not start at the center of the initial wave packet. This guiding ``off-center" trajectory is used to expand the local potential, controlling the propagating ``thawed" Gaussian wavepacket such that it is led to optimal overlap with a final state. Its simple and efficient performance in any number of dimensions heralds an exciting addition to the semiclassical tools available for quantum propagation. [Preview Abstract] |
Thursday, March 6, 2014 3:18PM - 3:30PM |
W27.00005: Behavior of the $GW$ approximation of Many-Body Pertubation Theory upon electron addition or removal Fabien Bruneval, Miguel Marques Within Many-Body Perturbation Theory (MBPT), the position of highest occupied molecular orbital (HOMO) is a quasiparticle energy. It should be hence stable upon an electron removal. The situation is slightly more complicated within Density-Functional Theory, for which the exchange-correlation potential may experience discontinuities. However, once this technicality has been considered, the HOMO energy should also be stable [1]. In other words, within an exact theory, the LUMO of a positive ion should be equal to the HOMO of the neutral molecule. It is remarkable that most approximations within DFT and MBPT fail with this sanity check. Here we demonstrate for isolated atoms and molecules that the $GW$ approximation, though not perfect, presents the weakest deviation from the ideal behavior among all the approximation studied [2]. The results have been obtained with a newly developed $GW$ code based on the Gaussian basis, which does not employ any further technical approximation besides the basis set [3]. We show that the convergence is unexpectedly slow, in constrast with earlier reports. \\[4pt] [1] A.J. Cohen, P. Mori-Sanchez, and W.T. Yang, Science 321, 792 (2008).\\[0pt] [2] F. Bruneval, JCP 136, 194107 (2012).\\[0pt] [3] F. Bruneval and M.A.L. Marques, JCTC 9, 324 (2013). [Preview Abstract] |
Thursday, March 6, 2014 3:30PM - 3:42PM |
W27.00006: Single-site density matrix embedding theory: from one to infinite dimensions Zhengqian Cheng, Chris Marianetti The recently developed density matrix embedding theory (DMET) has proven to be reliable for ground state properties in the Hubbard model in one and two dimensions. Here we focus on the single-site DMET, which has potential as a highly efficient method to treat actinides and oxides. We apply DMET in infinite dimensions where it can be compared to the exact solution via the dynamical mean-field theory. The results for the single band model, in addition to the two-band model with exchange and a crystal-field will be presented. Different magnetic solutions will also be presented in 1D, 2D, and infinite dimensions. We show that single-site DMET can be very reliable if one allows for magnetic solutions. [Preview Abstract] |
Thursday, March 6, 2014 3:42PM - 3:54PM |
W27.00007: Many-Body Density Matrix Theory C.J. Tymczak, Kostyantyn Borysenko We propose a novel method for obtaining an accurate correlated ground state wave function for chemical systems beyond the Hartree-Fock level of theory. This method leverages existing linear scaling methods to accurately and easily obtain the correlated wave functions. We report on the theoretical development of this methodology, which we refer to as Many Body Density Matrix Theory. This theory has many significant advantages over existing methods. One, its computational cost is equivalent to Hartree-Fock or Density Functional theory. Two it is a variational upper bound to the exact many-body ground state energy. Three, like Hartree-Fock, it has no self-interaction. Four, it is size extensive. And five, formally is scales with the complexity of the correlations that in many cases scales linearly. We show the development of this theory and give several relevant examples. [Preview Abstract] |
Thursday, March 6, 2014 3:54PM - 4:06PM |
W27.00008: Energy density matrix decomposition of interacting quantum systems Jaron Krogel, Jeongnim Kim, Fernando Reboredo We develop energy density matrices that parallel the one-body reduced density matrix for many-body quantum systems. Just as the density matrix gives access to the number density and orbital occupations, the energy density matrix yields the energy density and orbital energy levels. The eigenvectors of the matrix provide a natural orbital partitioning of the energy density while the eigenvalues comprise a single particle like energy spectrum obeying a total energy sum rule. In systems where a single particle picture is valid (e.g. for mean-field or weak interactions), the spectrum gives the expected results. We demonstrate that the QMCPACK implementation of the energy density matrix approach is correct for the cases of the non-interacting electron gas and the spherical harmonic oscillator. We further explore the meaning of the computed spectrum in the case of the fully interacting electron gas. [Preview Abstract] |
Thursday, March 6, 2014 4:06PM - 4:18PM |
W27.00009: Precise estimate of correlation length exponents from simple real-space renormalization group analysis Aleksander Kubica, Beni Yoshida We invent a novel real-space renormalization group (RG) scheme which accurately estimates correlation length exponents $\nu$ near criticality of quantum Ising and clock models in higher dimensions. The method, based on a recent proposal by Miyazaki et al., Phys. Rev. E 83, 051103 (2011), is remarkably simple (often analytical), grouping only a few spins into a block spin so that renormalized Hamiltonian has a closed form. A previous difficulty of spatial anisotropy and unwanted terms arising in higher-dimensional RG schemes is avoided by incorporating rotational invariance and internal $Z_q$ symmetries of the Hamiltonian. By applying this scheme to (2+1)-dim Ising model on a triangular lattice, we obtained $\nu=0.6300$ which is within statistical error of the current best Monte-Carlo result and $\phi^4$ theory estimation with seven-loop corrections. We also apply the scheme to higher-dimensional clock (Potts) models for which ordinary Monte-Carlo methods are not efficient due to suppression of quantum fluctuation in first-order phase transition. [Preview Abstract] |
Thursday, March 6, 2014 4:18PM - 4:30PM |
W27.00010: Nearest neighbor interaction in the Path Integral Renormalization Group method Wasanthi De Silva, R. Torsten Clay The Path Integral Renormalization Group (PIRG) method is an efficient numerical algorithm for studying ground state properties of strongly correlated electron systems. The many-body ground state wave function is approximated by an optimized linear combination of Slater determinants which satisfies the variational principle. A major advantage of PIRG is that is does not suffer the Fermion sign problem of quantum Monte Carlo. Results are exact in the noninteracting limit and can be enhanced using space and spin symmetries. Many observables can be calculated using Wick's theorem. PIRG has been used predominantly for the Hubbard model with a single on-site Coulomb interaction $U$. We describe an extension of PIRG to the extended Hubbard model (EHM) including $U$ and a nearest-neighbor interaction $V$. The EHM is particularly important in models of charge-transfer solids (organic superconductors) and at $\frac{1}{4}$-filling drives a charge-ordered state. The presence of lattice frustration also makes studying these systems difficult. We test the method with comparisons to small clusters and long one dimensional chains, and show preliminary results for a coupled-chain model for the (TMTTF)$_2$X materials. [Preview Abstract] |
Thursday, March 6, 2014 4:30PM - 4:42PM |
W27.00011: Correlation effects in metallic cohesion Roger Haydock The electronic contribution to the cohesive energy of a correlated metal is the sum of the transition energies for adding successive electrons at successive Fermi levels until the system reaches its final electron density. This can be computed as the integral of energy over the projected density of transitions for adding single electrons to localized orbitals. In the case of independent electrons, this reduces to the usual integral over the projected density of states. As an example, cohesive energies for some simple transition metal structures are calculated using the recursion method$^{\ast }$ with a Hubbard repulsion between electrons. * Phys. Rev. B \underline {61}, 7953-64 [Preview Abstract] |
Thursday, March 6, 2014 4:42PM - 4:54PM |
W27.00012: Local susceptibility and Kondo scaling Andreas Weichselbaum, Markus Hanl The Kondo scale $T_K$ for quantum impurity systems is typically assumed to guarantee universal scaling of physical quantities. In practice, however, not every definition of $T_K$ necessarily supports this notion away from the strict scaling limit for finite bandwidth $D$. Various theoretical definitions of $T_K$ are analyzed based on the inverse magnetic impurity susceptibility at zero temperature. While conventional definitions in that respect quickly fail to ensure universal Kondo scaling for all $D$, an altered definition of $T_K^{\mathrm{sc}}$ is presented which allows universal scaling of dynamical or thermal quantities for a given fixed Hamiltonian. If the scaling is performed with respect to an external parameter which directly enters the Hamiltonian, such as magnetic field, the corresponding $T_K^{\mathrm{sc,B}}$ for universal scaling may differ, yet becomes equivalent to $T_K^{\mathrm{sc}}$ in the scaling limit. The only requirement for universal scaling in the full Kondo parameter regime with a residual error of less than $1\%$ is a well-defined isolated Kondo feature with $T_K\leq 0.01\,D$. By varying $D$ over a wide range relative to the bare energies of the impurity, this allows a smooth transition from the Anderson to the Kondo model. [Preview Abstract] |
Thursday, March 6, 2014 4:54PM - 5:06PM |
W27.00013: Study of Electron Distribution and Magnetism at the Relaxed SrTiO$_3$/LaAlO$_3$ Interface Soham Ghosh, Efstratios Manousakis The presence of a two-dimensional electron gas (2DEG) at the interface between two insulators SrTiO$_3$ and LaAlO$_3$ makes it an interesting topic of condensed matter research. It exhibits a variety of properties such as high mobility, magnetism and superconductivity. Bandstructure calculations have linked the presence of the electon gas to polar catastrophe and oxygen vacancy, but the value of the carrier density and its distribution is a matter of debate. In the present work, we use Density Functional Theory to study the electron density distribution and the effect of ionic relaxations on the properties of the 2DEG. In order to understand the nature of magnetism, we construct localized Wannier functions from Bloch states given by DFT and use them to calculate hopping matrix elements and exchange integrals, which act as parameters in a model to understand electron-electron correlation at the interface. [Preview Abstract] |
Thursday, March 6, 2014 5:06PM - 5:18PM |
W27.00014: Electronic and optical properties of $LaVO3$ and $LaVO3$/$SrTiO3$ interface using Ab Initio techniques Suvadip Das, Efstratios Manousakis We have investigated the electronic structure and optical anisotropy of the strongly correlated system $LaVO_3$ using DFT+U and Many body perturbation theory (MBPT) techniques implemented by the Vienna Ab Initio Simulation Package (VASP) code. LDA+U predicts $LaVO_3$ to be an antiferromagnetic insulator with C-type spin and G-type orbital ordering in the monoclinic phase. We will discuss the nature of the transitions leading to the in-plane and out of plane anisotropy in the optical conductivity of $LaVO_3$ using GGA+U. The GW self-energy correction have been incorporated by solving the quasiparticle energies self consistently and the two particle-hole excitonic effects have been included by further solving the Bethe Salpeter equations (BSE). The electronic structure and nature of the low energy optical peaks and their dependence on temperature in the $LaVO_3$/$SrTiO_3$ interface will be presented. The prospect of using $LaVO3$/$SrTiO3$ as a photovoltaic cell with enhanced photo current by the generation of multiple elctron-hole pairs will also be discussed. [Preview Abstract] |
Thursday, March 6, 2014 5:18PM - 5:30PM |
W27.00015: The Extended Haldane Phase in Bilinear-Biquadratic Spin-1 chains Colin West, Artur Garcia-Saez, Tzu-Chieh Wei We study the gap of the Haldane phase in the biliniear-biquadratic model as parameterized by $\beta$, the coefficient of the biquadratic term. We then investigate the effect of additional local perturbations on the phase diagram, as first studied at $\beta = 0$ by Gu \& Wen [PRB 80, 155131 (2009)], and later by Pollmann \& Turner [PRB 86, 125441, (2012)]. In particular, we explore the extended Haldane phase under such perturbations, using the guidance of the perturbation-free gap, Pollmann-Turner topological order parameters, and other physical quantities. [Preview Abstract] |
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