Bulletin of the American Physical Society
APS March Meeting 2010
Volume 55, Number 2
Monday–Friday, March 15–19, 2010; Portland, Oregon
Session B23: Strongly Correlated Systems I 
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Sponsoring Units: DCOMP Chair: Paul Kent, Oak Ridge National Laboratory Room: C125C126 
Monday, March 15, 2010 11:15AM  11:27AM 
B23.00001: Approximating strongly correlated spin and fermion wavefunctions with correlator product states Hitesh Changlani, Jesse Kinder, Cyrus Umrigar, Garnet Chan We describe correlator product states, a class of numerically efficient manybody wave functions to describe strongly correlated wave functions in any dimension. Correlator product states introduce direct correlations between physical degrees of freedom in a simple way, yet provide the flexibility to describe a wide variety of systems. Variational Monte Carlo calculations for the Heisenberg and spinless fermion Hubbard models demonstrate the promise of correlator product states for describing both twodimensional and fermion correlations. In one dimension, correlator product states appear competitive with matrix product states for the same number of variational parameters. [Preview Abstract] 
Monday, March 15, 2010 11:27AM  11:39AM 
B23.00002: The Truncated Eigenfermion Decomposition applied to the Hubbard model Jonathan Moussa, James Chelikowsky The Truncated Eigenfermion Decomposition provides a unified computational framework for the calculation of eigenvalues, reduced density matrices, and transition density matrices of manyfermion Hamiltonians. Computations are made tractable by truncating the manyfermion operator basis that is used to approximate transformed Hamiltonians. Operator bases of increasing size and computational complexity can be arranged in a hierarchy that enables a systematic reduction of truncation errors. The suitability of this formalism for the study of strongly correlated electrons is assessed by studying the Hubbard model on finite clusters. Results are presented as a function of operator basis size, cluster size, interaction strength, and doping. [Preview Abstract] 
Monday, March 15, 2010 11:39AM  11:51AM 
B23.00003: Finite holedoping of the $tJ$ and related models within the noncrossing approximation Satyaki Kar, Efstratios Manousakis The spin and hole dynamics in a 2D holedoped quantum antiferromagnet is studied for small but finite holedoping fractions within the twodimensional $tJ$ and the related $tt^\primet^{\prime\prime}J$ model. The noncrossing approximation is used to sum up the selfenergy diagrams and the Dyson's equations for both the hole and magnon Green's functions are solved selfconsistently. The evolution with doping of the hole and magnon spectra with doping is determined, the Fermi surface topology is studied and the dopingdependent staggered magnetization of the system is computed. The latter determines the doping fraction up to which the spin wave theory remains a reasonable approximation to describe the doped antiferromagnet. [Preview Abstract] 
Monday, March 15, 2010 11:51AM  12:03PM 
B23.00004: Hybrid Monte Carlo scheme for interacting doubleexchange systems Malcolm Kennett, Nuri Yazdani The magnetic and electronic properties of diverse systems such as diluted, magnetic semiconductors, manganites and europium hexaboride can be described using kineticexchange models in which itinerant carriers are coupled to local magnetic moments. Monte Carlo simulations of the magnetic properties of such models usually treat the local moment spins as classical and ignore electronelectron interactions due to the need to diagonalize a fermion problem at each spin flip. We introduce a hybrid Monte Carlo scheme that allows electronelectron interactions to be included at a mean field level. We identify regions in parameter space where our approach is most useful and present results of simulations of thermodynamic quantities in ordered and disordered models of interacting fermions coupled to local moments. [Preview Abstract] 
Monday, March 15, 2010 12:03PM  12:15PM 
B23.00005: A New Numerical Approach Toward MPS State on Spin Ladder Systems Zhenyue Zhu, Steven White The matrix product state (MPS) representation used by DMRG is extremely effective in 1D, but loses effectiveness exponentially with the width in ladder systems. Tensor product wavefunction, such as PEPS, are efficient representations of 2D states but calculations utilizing them are very inefficient. As an intermediate approach between these, we consider a wavefunction consisting of an MPS multiplied by local bond exponentials $^{}\tau H_{bond}$ applied on adjacent sites in the lattice which appear distant in the MPS. The exponentials restore the area law to the MPS. For efficient calculation, the bondexponentials are transferred to the Hamiltonian in a matrix product operator representation, acting as a similarity transformation, preserving the eigenvalues. For this method to be successful, not only should the modified MPS representation be efficient, the MPO representation of the transformed Hamiltonian should have a small matrix dimension. We report on preliminary results on ladders with several legs for this approach. [Preview Abstract] 
Monday, March 15, 2010 12:15PM  12:27PM 
B23.00006: Time Evolution of Correlator Product States Jesse M. Kinder, Garnet KinLic Chan, Hitesh Changlani, Eric Neuscamman, Cyrus J. Umrigar Correlator product states are a class of manybody wave functions that allow the efficient numerical simulation of strongly correlated systems in any dimension. We have developed algorithms to approximate the time evolution of correlator product states. Evolution in imaginary time projects an arbitrary wave function onto the ground state of the system. Real time evolution simulates the dynamics of a system and can be used to construct the spectral density function. We present studies of the time evolution of correlator product states for the Heisenberg model in one, two, and three dimensions. [Preview Abstract] 
Monday, March 15, 2010 12:27PM  12:39PM 
B23.00007: Numerical investigations of frustrated itinerant electrons Matthew Enjalran Frustration has been a major topic in the study of magnetism for decades. Its presence in material systems is linked to the realization of exotic phases of matter  spin glasses, spin ices, spin liquids. With the recent discovery of several geometrically frustrated itinerant electron materials, where the relevant physics occurs on a lattice constructed from connected triangles, the role of frustration in interacting Fermi systems has become an increasingly important question. Numerical methods have been indispensable in the development of our understanding of frustrated magnets. The same will certainly hold for the study of frustrated itinerant electrons. From this perspective, we use several numerical techniques to study the frustrated Hubbard model. Our initial concerns are to explore the general physics of the frustrated Hubbard model at halffilling and to test the effectiveness of different numerical techniques in the presence of frustrating interactions. Particular emphasis is placed on the application of the constrained path/phase quantum Monte Carlo method to the frustrated Hubbard model. [Preview Abstract] 
Monday, March 15, 2010 12:39PM  12:51PM 
B23.00008: An intermediate model for cuprates Shiu Liu, Steven White We propose an effective twoband model, which is similar to the model considered previously by Frenkel, Gooding, Shraiman, and Siggia (PRB 41, number 1, page 350), for describing highT$_c$ superconducting cuprates. Instead of rotating away all oxygen states to construct the effective sites in the Hubbard or tJ model, we keep all oxygens allowing the hopping of the doped holes under an antiferromagnet background on the copper sites. This approach will be useful to explain STM experimental data which resolves the oxygen atoms (for example, Hanaguri et al Nature 3, 865. 2007). The magnitudes of the interactions in twoband model are derived from a threeband Hubbard model with reasonable parameters by applying numerical canonical transformations with appropriate truncations. The proposed twoband model is studied by applying DMRG calculation for different lattices, such as ladders, and the results are compared with same calculations done for three band model. [Preview Abstract] 
Monday, March 15, 2010 12:51PM  1:03PM 
B23.00009: Fast Update Algorithm for Quantum Monte Carlo Simulations of the Hubbard Model Phani K.V.V. Nukala, Thomas A. Maier, Michael S. Summers, Gonzalo Alvarez, Thomas C. Schulthess This paper presents an efficient algorithm for computing the transition probability in auxiliary field quantum Monte Carlo simulations of strongly correlated electron systems using a Hubbard model. This algorithm is based on a lowrank updating of the underlying linear algebra problem, and results in significant computational savings. The computational complexity of computing the transition probability and Green's function update reduces to $O(k^2)$ during the $k$th step, where $k$ is the number of accepted spin flips, and results in an algorithm that is faster than the competing delayed update algorithm. Moreover, this algorithm is orders of magnitude faster than traditional algorithms that use naive updating of the Green's function matrix. [Preview Abstract] 
Monday, March 15, 2010 1:03PM  1:15PM 
B23.00010: Selfconsistent solution of the Hubbard model on a 4x4 cluster with the parquet formalism Herbert Fotso, Shuxiang Yang, Jun Liu, Mark Jarrell, Eduardo D'Azevedo, Thomas Maier, Karen Tomko, Richard Scalettar, Thomas Pruschke A selfconsistent solution of the Hubbard model is performed on a 4x4 cluster at both the one and the twoparticle level. We combine the Parquet and the BetheSalpeter equations into one nonlinear equation to take advantage of optimized linear solvers such as GMRES and BICGStab. We calculate some relevant quantities and compare them to the results obtained from Determinant Quantum Monte Carlo (DQMC), selfconsistent second order approximation and FLuctuation EXchange (FLEX) approximation. We find that the parquet approximation, where the fully irreducible vertex is approximated by the bare vertex, shows satisfactory agreement with DQMC and a significant improvement from FLEX or selfconsistent second order approximation. [Preview Abstract] 

B23.00011: ABSTRACT WITHDRAWN 
Monday, March 15, 2010 1:27PM  1:39PM 
B23.00012: Second Renormalization of TensorNetwork States Tao Xiang We propose a second renormalization group method to handle the tensornetwork states or models. This method dramatically reduces the truncation error of the tensor renormalization group. It allows physical quantities of classical tensor network models or tensornetwork ground states of quantum systems to be accurately and efficiently determined. References: [1] H.C. Jiang, Z.Y. Weng, T. Xiang, Phys. Rev. Lett. 101, 090603 (2008). [2] Z. Y. Xie, H. C. Jiang, Q. N. Chen, Z. Y. Weng, T. Xiang, Phys. Rev. Lett. 103, 160601 (2009). [Preview Abstract] 
Monday, March 15, 2010 1:39PM  1:51PM 
B23.00013: Quantum criticality in the 2D Hubbard: from weak to strong coupling Dimitrios Galanakis, Karlis Mikelsons, Ehsan Khatami, Peng Zhang, Zhaoxin Xu, Juana Moreno, Mark Jarrell We study the phase diagram of the twodimensional Hubbard model in the vicinity of the quantum critical point which separates the fermi liquid from the pseudogap region. We use the Dynamical Cluster Approximation (DCA) in conjunction with the weakcoupling continuous time quantum Monte Carlo (CTQMC) cluster solver. We measure the filling $n_c$ and the density of states at the critical point as a function of the Coulomb interaction $U$. We observe a change in behavior when the Coulomb interaction is of the order of the bandwidth. We also evaluate the temperature range in which the system is under the influence of the quantum critical point and compare it with the effective spin coupling $J_{eff}$. We discuss the consistency of these results with various mechanisms of quantum criticality. This research is supported by NSF DMR0706379 and OISE0952300. [Preview Abstract] 
Monday, March 15, 2010 1:51PM  2:03PM 
B23.00014: Diffusion and ballistic transport in onedimensional quantum systems Jesko Sirker, Rodrigo Pereira, Ian Affleck It has been conjectured that transport in integrable onedimensional (1D) systems is necessarily ballistic. The large diffusive response seen experimentally in nearly ideal realizations of the $S=1/2$ 1D Heisenberg model is therefore puzzling and has not been explained so far. Here, we show that, contrary to common belief, diffusion is universally present in interacting 1D systems subject to a periodic lattice potential. We present a parameterfree formula for the spinlattice relaxation rate which is in excellent agreement with experiment. Furthermore, we calculate the current decay directly in the thermodynamic limit using a timedependent density matrix renormalization group algorithm and show that an anomalously large time scale exists even at high temperatures.\\*[0.5cm] J. Sirker, R.G. Pereira, I. Affleck, PRL (2009, in print) [Preview Abstract] 
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