Bulletin of the American Physical Society
APS March Meeting 2019
Volume 64, Number 2
Monday–Friday, March 4–8, 2019; Boston, Massachusetts
Session V16: Quantum Manybody Systems: Theory and Computation IIFocus

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Sponsoring Units: DCOMP Chair: Lea Santos, Yeshiva University Room: BCEC 155 
Thursday, March 7, 2019 2:30PM  2:42PM 
V16.00001: OffDiagonal Expansion Quantum Monte Carlo Itay Hen, Tameem Albash, Lalit Gupta I will discuss a novel, parameterfree Trotter errorfree, quantum Monte Carlo technique designed to tackle a very broad range of physical models within a single unifying framework. The method builds on a series expansion of the canonical partition function around its classical component. The expansion further allows for a grouptheoretical abstraction of the QMC algorithm. Some results showcasing the capabilities of the algorithm will be presented. 
Thursday, March 7, 2019 2:42PM  2:54PM 
V16.00002: FInitetemperature AuxiliaryField Quantum Monte Carlo: Recent Developments and Applications YuanYao He, Mingpu Qin, Hao Shi, ZhongYi Lu, Shiwei Zhang We present a highly accurate auxiliaryfield quantum Monte Carlo (AFQMC) method to study finitetemperature properties of correlated fermion systems. This approach eliminates the minus sign problem by introducing constraints in auxiliaryfield space. Building on earlier ideas [1] and incorporating the latest developments in zerotemperature methods, we introduce a selfconsistent formalism [2] to improve the constraint in the finitetemperature framework. This with several other algorithmic advances leads to a more accurate, more efficient, and numerically more stable approach for finitetemperature calculations. We carry out systematic benchmark study in the 2D Hubbard model. Temperatures as low as T=1/80 (in units of hopping) are reached. The finitetemperature method is exact at high temperatures, and approaches the result of the zerotemperature constrainedpath AFQMC as temperature is lowered. The benchmark shows that systematically accurate results are obtained for thermodynamic properties. The properties of the 2D doped Hubbard model as functions of temperature will be presented and discussed. 
Thursday, March 7, 2019 2:54PM  3:06PM 
V16.00003: Application of the linked cluster expansion to the manyparticle pathintegral Anish Bhardwaj, Efstratios Manousakis A diagrammatic expansion for the pair distribution can be derived by starting from the manybody pathintegral and using the idea of cluster expansion. The expansion is written as a sum of nodal and nonnodal diagrams. The sum of all the nodal diagrams can be expressed in terms of the nonnodal diagrams using the hypernetted equation technique. The sum of the nonnodal diagrams, which are irreducible diagrams in momentum space, are written as a perturbation expansion in powers of the particle density. Our approach is analogous to the wellknown manybody perturbation expansion of the nbody Green's function. The approach was tested on a system of distinguishable particles and our results agree very well with those obtained from the pathintegral Monte Carlo. 
Thursday, March 7, 2019 3:06PM  3:18PM 
V16.00004: A multiprojective variational approach to the quantum lattice problem Zhengqian Cheng, Chris Marianetti We formulate a general method for constructing a variational expression of the total energy based on two projective ansatz from the weak and strong coupling limits. These two ansatz are then combined according to individual and mutual interactions of low and high energy degrees of freedom. We apply our approach to the single band Hubbar model, where the theory yields the double occupancy and the nonlocal singleparticle density matrix. We compare to exact results for d=1 and d=infinity. For d=1, the insulating state is properly obtained at infinitesimal u; in addition to an accurate prediction of the ground state energy over a broad range of t/U. In infinite dimensions, we properly find a finiteU metalinsulator transition with reasonable quantitative accuraccy across all parameter space. Our approach has a negligible computational cost as compared to dynamical mean field theory and could be highly applicable in the context of total energies for strongly correlated materials and molecules. 
Thursday, March 7, 2019 3:18PM  3:30PM 
V16.00005: New practical methods for consistently closing truncated equations of motion Johan Nilsson We discuss some new methods for truncating and closing the equations of motion for composite operators. Our formalism automatically generates a physical theory in the sense of having positive spectral weights. Another important advantage of our methods is that (for judiciously chosen set of operators) all averages necessary to close the formalism can be calculated selfconsistently from within the theory itself. We discuss how the method can be applied to the Hubbard model in both fermionic and bosonic sectors. 
Thursday, March 7, 2019 3:30PM  3:42PM 
V16.00006: Semilocal observables from importance sampling diffusion Monte Carlo Fernando Reboredo An approach to evaluate a family of semilocal observables from the fixednode ground state will be discussed. The celebrated importancesampling diffusion Monte Carlo (DMC) method by Ceperley and Alder is a real space approach. Therefore, beyond the calculation of the total energy of the fixednode ground state, DMC facilitates the evaluation of observables that are local in real space such as the density, albeit pure estimators or extrapolations are required. The evaluation of semilocal observables is expected to be more involved. It can be shown, however, that the DMC algorithm carries additional information of the fixednode solution. DMC results for semilocal operators will be compared with exact results, in the hydrogen atom and the harmonic oscillator. The perspectives, computational cost, and potentials problems of this approach when applied to realistic manybody systems will be discussed. 
Thursday, March 7, 2019 3:42PM  3:54PM 
V16.00007: Accurate total energies of pseudopotentials Abdulgani Annaberdiyev, Cody Melton, Michael Bennett, Guangming Wang, Lubos Mitas We present high accuracy total energies of pseudoatoms, i.e, atoms with effective core potentials (ECP). The pseudoatoms considered are the 1st, 2nd and 3rdrow elements with correlation consistent effective core potentials (ccECP) we constructed. For each element, we perform configuration interaction, coupledcluster, and quantum Monte Carlo calculations with systematically eliminated/improved errors. 
Thursday, March 7, 2019 3:54PM  4:06PM 
V16.00008: Compton Profile of Solid and Liquid Lithium from Quantum Monte Carlo Yubo Yang, Markus Holzmann, David M Ceperley Compton scattering cross section is directly related to the electronic momentum distribution and provides an important check of manybody theory. We computed the Compton profile of solid and liquid lithium using quantum Monte Carlo (QMC) and compared with recent experiments obtaining excellent agreement. Importantly, we find it necessary to explicitly include the core electrons for quantitative accuracy. To account for lattice effects, we sampled finitetemperature configurations using molecular dynamics (MD), then performed pseudopotential diffusion Monte Carlo (DMC) simulations on each configuration. We used SlaterJastrow wavefunction and twistaveraged boundary condition. QMC pseudopotential correction was derived from an allelectron DMC simulation of the perfect crystal. Our calculations provide the first allelectron QMC benchmark for the Compton profile of lithium under both liquid and solid conditions. 
Thursday, March 7, 2019 4:06PM  4:18PM 
V16.00009: Prediction of the singlettriplet excitation energy for the spinel, MgTi_{2}O_{4} via downfolding approach combined with firstprinciples Quantum Monte Carlo Brian Busemeyer, Greg MacDougall, Lucas Wagner The spinel, MgTi_{2}O_{4} undergoes a transition into a dimerized state at low temperatures that is expected to be a spin singlet. However, no signature of a singlettriplet transition as been discovered, in part due to the difficulty of predicting the energy of the transition from theory. Using highaccuracy firstprinciples quantum Monte Carlo combined with a novel modelfitting approach, we predict the singlettriplet gap to be 350(50) meV, a higher energy than previous experimental observations have considered. Confirmation of our prediction would suggest that our approach should enable calculation of other excitation energies on the basis of firstprinciples quantum Monte Carlo combined with effective model calculations. 
Thursday, March 7, 2019 4:18PM  4:30PM 
V16.00010: An Efficient Calculation of the Total Energy Variation in DFT+DMFT Implemented using Orthogonal Basis sets Benny Wah, Hyowon Park Calculations of the total energy variation in density functional theory plus dynamical mean field theory (DFT+DMFT) with respect to the structural change are important for atomic force and stress computations for strongly correlated materials. In this talk, we will show that the energy variation of DFT+DMFT implemented using orthogonal basis sets such as Wannier functions can be computed efficiently using analytic formula since the potential energy variation can be exactly cancelled out and the DMFT selfenergy itself or its variation does not need to be explicitly accounted. We will use DMFT with the ContinuousTime Quantum Monte Carlo (CTQMC) impurity solver to compute its total energy variation of the twodimensional oneband Hubbard model with respect to changes of hopping parameters and compare to the results of its analytic energy derivative formula to verify their quantitative agreement. We will also compare the potential energy contributions sampled directly from CTQMC and computed using the MigdalGalitzki formula. The application of our formula to the calculations of forces and stress in DFT+DMFT will be also discussed. 
Thursday, March 7, 2019 4:30PM  4:42PM 
V16.00011: Systematic corrections to the ThomasFermi approximation without a gradient expansion Jun Hao Hue, Thanh Tri Chau, MartinIsbjörn Trappe, Berge Englert We improve on the Thomas–Fermi approximation for the single particle density of fermions by introducing inhomogeneity corrections. Rather than invoking a gradient expansion, we relate the density to the unitary evolution operator for the given effective potential energy and approximate this operator by a Suzuki–Trotter factorization. This yields a hierarchy of approximations, one for each approximate factorization. For the purpose of a first benchmarking, we examine the approximate densities for a few cases with known exact densities and observe a very satisfactory, and encouraging, performance. As a bonus, we also obtain a simple fourthorder leapfrog algorithm for the symplectic integration of classical equations of motion. 
Thursday, March 7, 2019 4:42PM  4:54PM 
V16.00012: Approximate States of the Hubbard Model from Heisenberg's Equation Roger Haydock Operators which add electrons with definite energies to states of interacting electrons are solutions of the timeindependent Heisenberg equation. Expanding the operators in the number of electronhole pairs generated to screen each added electron provides systematic approximations for the energies of these operators. This is illustrated for the simplest Hubbard model on a cubic lattice by relations between the energies and electron densities of ground states. 

V16.00013: ABSTRACT WITHDRAWN

Thursday, March 7, 2019 5:06PM  5:18PM 
V16.00014: Correlated states in magnetic quantum dots with multiple occupancy Tiago De Campos, James Pientka, Alex Matos Abiague, Jong E Han, Igor Zutic The motivation to magnetically dope semiconductor quantum dots comes from the possibility for an enhanced control of magnetic ordering as compared to their bulklike counterparts. Unlike in the bulk structures, adding a single carrier in a magnetic QD can have important ramifications. An extra carrier can both strongly change the total carrier spin and the temperature of the onset of magnetization[1]. While QDs have been recognized for correlation effects, inherent in the analog of Wigner crystals referred to as Wigner molecules (WMs), the modification of underlying correlated states with magnetic doping is largely unexplored[2]. By focusing on Mndoped IIVI QDs[3] we show correlated states, which can be viewed as a generalization of WMs, can be studied using exact diagonalization and conditional probability density. We explain how the formation of a shell structure in these Mndoped QDs and magnetic frustrations are altered by the changes in strength of the Coulomb interaction. 
Thursday, March 7, 2019 5:18PM  5:30PM 
V16.00015: Resilience of the Mixed State Wigner Function Albert Materdey, Thomas Materdey, Alexander Materdey Solution of the quantum Vlasov equation shows the phase space dynamics of a mixedstate Wigner function is more resilient against changes in external electric and magnetic fields than a purestate Wigner function. A particle in a mixedstate is harder to follow and localize, but the freedom to access a range of pure states increases its inertia against changes in external conditions. This could explain the electron's stability in the Shrodinger's atomic orbital model and perhaps provides a way to preserve the information of a qubit sufficiently long for quantum computing. 
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