1. 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

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

3. Aims of this study 1.Calculate excitation spectrum from first principles 2.Explore the nature of the excitations, i.e. are they related to vacancies, defects, localized modes, … Goals and Motivation Why Correlation Function Quantum Monte Carlo? 1.Used to obtain excitation energies for molecular vibrations and homogeneous electron gas 2.Both energies and excited state wavefunctions are available, providing more microscopic detail Carleo, et al., PRB 80, 094301 (2009)

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

5. 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 Correlation Function Quantum Monte Carlo D..M. Ceperley & B. Bernu, J. Chem. Phys. 89, 6316 (1988)

6. Interactions Many Body Basis Pair Potential Aziz, et al., Metrologia 27, 211 (1990) Aziz HFD-B2 Potential Site Excitations L.H. Nosanow, PR 146, 120 (1966) Modeling Crystalline Helium 1/r 10 10.9 K 1/r 6 Trial Ground State Crystal Symmetries Translation Symmetries Point Group Symmetries

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

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

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

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

11. 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 Conclusions and Future Work