Bulletin of the American Physical Society
APS March Meeting 2010
Volume 55, Number 2
Monday–Friday, March 15–19, 2010; Portland, Oregon
Session D23: Strongly Correlated Systems II |
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Sponsoring Units: DCOMP Chair: Randy Fishman, Oak Ridge National Laboratory Room: C125-C126 |
Monday, March 15, 2010 2:30PM - 2:42PM |
D23.00001: Applications of projected entangled-pair states to two-dimensional spin systems Bela Bauer, Guifre Vidal, Matthias Troyer The density matrix renormalization group and the class of states it operates on, matrix-product states, have been widely accepted to be among the most powerful methods for simulations of one-dimensional quantum systems. They allow reliable approximations to the ground states of many quantum systems and have recently been extended to allow the simulation of time evolution and finite-temperature states. Generalizations to two-dimensional systems have therefore long been sought after. Several classes of tensor-network states that extend the concepts of matrix-product states to higher dimensions have been proposed. The common underlying property is that by construction, they capture the scaling of ground-state entanglement for large classes of systems and are therefore expected to approximate the properties of ground states accurately. In this presentation, we focus on a specific class of states, namely projected entangled-pair states on infinite lattices. We first assess the accuracy of these states for non-frustrated spin systems by comparing with Quantum Monte Carlo results. Furthermore, we present applications to frustrated quantum spin systems in two dimensions. [Preview Abstract] |
Monday, March 15, 2010 2:42PM - 2:54PM |
D23.00002: Symmetry Breaking in Matrix-Product States Chen Liu, Anders Sandvik, Yu-Cheng Su, Ying-Jer Kao We consider matrix-product states for the transverse-field Ising chain of finite and infinite size $N$ and small matrix sizes $D=2-8$. The matrices are variationally optimized using several methods. For finite $N$, below the critical field, there are energy minimums for symmetric as well as symmetry-broken states. The energies cross at a field strength $h_c(N,D)$; thus the transition is first-order in this approximation. However, for $N \to \infty$ the transition is continuous for any $D$. We find that the asymptotic critical behavior is then always mean-field like (the magnetization exponent $\beta=1/2$), but a window of the exactly known power-law scaling ($\beta=1/8$) emerges as $D$ increases. We point out that even if the energy is optimized to the level of double precision ($\approx 10^{-12}$ relative error) there is significant finite-size smoothing of the magnetization curve. Higher precision is required to access the asymptotic critical behavior. [Preview Abstract] |
Monday, March 15, 2010 2:54PM - 3:06PM |
D23.00003: Grassman-number tensor network states and its renormalization Zhengcheng Gu, Frank Verstraete, Xiaogang Wen Traditional condensed matter physics is based on two theories: symmetry breaking theory for phases and phase transitions, and Fermi liquid theory for metals. Mean-field theory is a powerful method to describe symmetry breaking phases and phase transitions by assuming the ground state wavefunctions for many- body systems can be approximately described by direct product states. The Fermi liquid theory is another powerful method to study electron systems by assuming that the ground state wavefunctions for the electrons can be approximately described by Slater determinants. In this paper, we propose a new class of states: Grassman-number tensor product states. These states only need polynomial amount of information to approximately encode many-body ground states. Many classes of states, such as matrix/tensor product states (M/TPS), Slater determinant states, etc., are subclasses of Grassman-number tensor product states. However, calculating the physical quantities for these state can be exponential hard in general. To solve this difficulty, we develop the Grassman-tensor- entanglement renormalization group (GTERG) method to efficiently calculate the physical quantities. We demonstrate our algorithm by studying several simple fermion/boson models. [Preview Abstract] |
Monday, March 15, 2010 3:06PM - 3:18PM |
D23.00004: Valence Fluctuations and Quasiparticle Multiplets in Pu Chalcogenides and Pnictides Chuck-Hou Yee, Gabriel Kotliar, Kristjan Haule The spectra of Pu chalcogenides and pnictides are computed with LDA+DMFT and interpreted with the aid of valence histograms and slave-boson calculations. We find the chalcogenides are mixed-valent ($n_f = 5.2$) materials with a strongly $T$-dependent low-energy density of states and a triplet of quasiparticle peaks below the Fermi level. Furthermore, we predict a doublet of reflected peaks above the Fermi level. In the pnictides, the raising of $f^6$ states relative to $f^5$ suppresses valence fluctuations, resulting in integral-valent ($n_f = 5.0$) local moment metals. [Preview Abstract] |
Monday, March 15, 2010 3:18PM - 3:30PM |
D23.00005: DMRG study of the Kagome Antiferromagnetic Heisenberg Model Simeng Yan, Steven White We have used DMRG to study the {\$}S=1/2{\$} Heisenberg model on the Kagome lattice, using cylindrical boundary conditions and large clusters. We have focused on the spin gap and the presence or absence of the Valence Bond Crystal (VBC) order with a 36 unit cell as studied by Marston and Zeng, Singh and Huse, and others. Our results are probably the highest accuracy results for large clusters to date. Our extrapolated results find a finite spin gap with a value of about 0.05 J. To determine whether VBC order occurs, we calculated the ground states of a variety of clusters, some of which allow the 36 site VBC order, and others which do not allow it. For narrower cylinders (width $<$ 12) , the VBC patterns are found to vanish as the number of kept states increases. For wider systems, we do observe VBC ground states, but it is not always clear that the calculations have converged. The extrapolated energies of the two types of states are very close, within about 1{\%}. [Preview Abstract] |
Monday, March 15, 2010 3:30PM - 3:42PM |
D23.00006: ABSTRACT WITHDRAWN |
Monday, March 15, 2010 3:42PM - 3:54PM |
D23.00007: Implementing the SU(2) Symmetry for the DMRG Gonzalo Alvarez In the Density Matrix Renormalization Group (DMRG) algorithm (White, 1992), Hamiltonian symmetries play an important role. Using symmetries, the matrix representation of the Hamiltonian can be blocked. Diagonalizing each matrix block is more efficient than diagonalizing the original matrix. This talk will explain how the DMRG++ code\footnote{arXiv:0902.3185 or Computer Physics Communications {\bf 180} (2009) 1572-1578.} has been extended to handle the non-local $SU(2)$ symmetry in a model independent way. Improvements in CPU times compared to runs with only local symmetries will be discussed for typical tight-binding models of strongly correlated electronic systems. The computational bottleneck of the algorithm, and the use of shared memory parallelization will also be addressed. Finally, a roadmap for future work on DMRG++ will be presented. [Preview Abstract] |
Monday, March 15, 2010 3:54PM - 4:06PM |
D23.00008: Quantum Monte Carlo simulation of transition metal compounds employing the full Coulomb interaction Brigitte Surer, Philipp Werner, Matthias Troyer, Andreas Laeuchli, Emanuel Gull, Jan Kunes, Alexander Lichtenstein The recently developed Krylov implementation of the hybridization expansion impurity solver [arXiv:0908.0681] allows an efficient simulation of large multi-orbital models with full Coulomb interactions. In combination with density functional theory and dynamical mean field theory (DMFT) the method opens a way to investigate transition metal and actinide compounds from first principles. We will present applications of this algorithm to five-orbital models. [Preview Abstract] |
Monday, March 15, 2010 4:06PM - 4:18PM |
D23.00009: Fully self-consistent LDA+DMFT calculations in the projector augmented wave (PAW) framework Bernard Amadon, Marc Torrent The combination of Density Functional Theory (DFT) in the Local Density Approximation (LDA) and Dynamical Mean Field Theory (DMFT) has been used in the past years to understand properties of strongly correlated electron systems. Recently, implementations have emerged based on state-of-the art density functional theory codes. We present here a implementation of LDA+DMFT, using projected local orbitals, which includes full self-consistency on the electronic density, within the Projector Augmented Wave (PAW) framework. This thus opens the way to accurate calculations including relaxation with the simplicity of a plane wave code and the all-electron precision. We benchmark this implementation on correlated metals and insulators. [Preview Abstract] |
Monday, March 15, 2010 4:18PM - 4:30PM |
D23.00010: Calculation of nonequilibrium spectral functions in quantum dot systems using imaginary-time method Jong E. Han Quantum mechanics for nonequilibrium many-body effects is formulated in the imaginary-time formalism. In quantum dot systems, we extend the chemical potentials of the source and drain leads by including the Matsubara voltage, which makes it possible to compute equilibrium and nonequilibrium steady-state within the same conventional imaginary-time technique. While the formal equivalence of the imaginary-time and real-time Keldysh methods can be established, the main problem has been the numerical analytic continuation of the self-energy of mapping the Matsubara voltage to the real voltage. In this presentation, we compare the calculations from the Hirsch-Fye discrete-time quantum Monte Carlo (QMC) and the continuous-time QMC method which significantly improves the high frequency self-energy. Through a comparison of the methods, the high-frequency problem of the discrete-time QMC results is much improved by correctly including the effects of discontinuity in the Green functions. With these modifications, the analytic continuation becomes much more reliable and we discuss various aspects of numerical procedures of fitting numerical self-energy in the Kondo model. [Preview Abstract] |
Monday, March 15, 2010 4:30PM - 4:42PM |
D23.00011: Pump-probe photoemission spectroscopy of nonequilibrium correlated electrons Brian J. Moritz, Thomas P. Devereaux, James K. Freericks Extension of photoemission spectroscopy to the time domain, using pump-probe techniques, opens the possibility of observing electron dynamics on time-scales relevant for correlated processes. Using a generalization of dynamical mean field theory (DMFT) to nonequilibrium problems, we study temporal evolution of the single-particle response of the Falicov-Kimball model subject to strong driving fields approximating the effect of a finite temporal pump-pulse on the electronic system. This approach captures the redistribution of spectral intensity amongst the accessible nonequilibrium electronic states that accompanies fields with these high excitation densities. We discuss the behavior of the response prior to, coincident with, and following the pump-pulse and comment on the applicability of the ``hot'' electron model or ``melting'' of the Mott gap within each regime, focusing particular attention on the evolution of the response following the pump-pulse. [Preview Abstract] |
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