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Hunting Anomalous Excitations in BCC Helium-4

Hunting Anomalous Excitations in BCC Helium-4. Jaron T. Krogel 1 Saad Khairallah 2 David Ceperley 1 1 Department of Physics, University of Illinois at Urbana-Champaign, Urbana, IL 2 Lawrence Livermore National Laboratory, Livermore, CA. Neutron Scattering Experiments.

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Hunting Anomalous Excitations in BCC Helium-4

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  1. Hunting Anomalous Excitations in BCC Helium-4 Jaron T. Krogel1 Saad Khairallah2 David Ceperley1 1Department of Physics, University of Illinois at Urbana-Champaign, Urbana, IL 2Lawrence Livermore National Laboratory, Livermore, CA

  2. Neutron Scattering Experiments Discovery of HOB along 110 Discovery of LOB & HOB along 111 . Markovich, et al. PRL 88, 19 (2002) Pelleg, et al. PRB 73, 180301 (2006)

  3. Goals and Motivation Aims of this study • Calculate excitation spectrum from first principles • Explore the nature of the excitations, i.e. are they related to vacancies, defects, localized modes, … Why Correlation Function Quantum Monte Carlo? • Used to obtain excitation energies for molecular vibrations and homogeneous electron gas • Both energies and excited state wavefunctions are available, providing more microscopic detail Carleo, et al., PRB 80, 094301 (2009)

  4. Correlation Function Quantum Monte Carlo Variational Theorem Imaginary Time Projection Many Body Basis Projected Basis Rayleigh Quotient Projected Eigenvalues Generalized Eigenvalue Problem are strict upper bounds to , for t large J.K.L. MacDonald, PR 43, 830 (1933)

  5. Correlation Function Quantum Monte Carlo Brief Overview of CFQMC Implementation • Single random walk samples guiding function • Basis states and local energies saved in imaginary time histories • Matrix elements appear as 2-point correlation functions D..M. Ceperley & B. Bernu, J. Chem. Phys. 89, 6316 (1988)

  6. Modeling Crystalline Helium Many Body Basis Interactions Trial Ground State Pair Potential Site Excitations Aziz HFD-B2 Potential L.H. Nosanow, PR 146, 120 (1966) 1/r10 1/r6 Crystal Symmetries 10.9 K Translation Symmetries Point Group Symmetries Aziz, et al., Metrologia 27, 211 (1990)

  7. Modeling Crystalline Helium Crystal Momentum Simultaneous Diagonalization Crystal Momentum Operator K Basis Representation Crystal Momentum Eigenvalues

  8. Results: Eigenvalue Convergence 54 atom cell (3x3x3 unit cells)

  9. Results: Dispersion Relation Legend Black (Exp Ac) Red (Exp Opt) Blue o (CFQMC) Composite 54 (3x3x3) 128 (4x4x4) 250 (5x5x5)

  10. Results: Dispersion Relation Legend Black (Exp Ac) Red (Exp Opt) Blue o (CFQMC) Composite 54 (3x3x3) 128 (4x4x4) 250 (5x5x5)

  11. Conclusions and Future Work Conclusions • A site local basis appears to sufficiently describe acoustic modes • Lower optic branch unobserved, perhaps qualitative differences • Possible sighting of higher optic modes Future Work • Investigate higher optic mode with longer projection in smaller cell • Compute real space density to assess the nature of the excitations *Supported by DOE Endstation Grant: DOE-DEFG05-08OR23336

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