Browsing by Author "Shepherd, James J."

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    Coupled cluster channels in the homogeneous electron gas
    (AIP Publishing, 2014) Shepherd, James J.; Henderson, Thomas M.; Scuseria, Gustavo E.
    We discuss diagrammatic modifications to the coupled cluster doubles (CCD) equations, wherein different groups of terms out of rings, ladders, crossed-rings, and mosaics can be removed to form approximations to the coupled cluster method, of interest due to their similarity with various types of random phase approximations. The finite uniform electron gas (UEG) is benchmarked for 14- and 54-electron systems at the complete basis set limit over a wide density range and performance of different flavours of CCD is determined. These results confirm that rings generally overcorrelate and ladders generally undercorrelate; mosaics-only CCD yields a result surprisingly close to CCD. We use a recently developed numerical analysis [J. J. Shepherd and A. Grüneis, Phys. Rev. Lett. 110, 226401 (2013)] to study the behaviours of these methods in the thermodynamic limit. We determine that the mosaics, on forming the Brueckner one-body Hamiltonian, open a gap in the effective one-particle eigenvalues at the Fermi energy. Numerical evidence is presented which shows that methods based on this renormalisation have convergent energies in the thermodynamic limit including mosaic-only CCD, which is just a renormalised MP2. All other methods including only a single channel, namely, ladder-only CCD, ring-only CCD, and crossed-ring-only CCD, appear to yield divergent energies; incorporation of mosaic terms prevents this from happening.
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    Range-Separated Brueckner Coupled Cluster Doubles Theory
    (American Physical Society, 2014) Shepherd, James J.; Henderson, Thomas M.; Scuseria, Gustavo E.
    We introduce a range-separation approximation to coupled cluster doubles (CCD) theory that successfully overcomes limitations of regular CCD when applied to the uniform electron gas. We combine the short-range ladder channel with the long-range ring channel in the presence of a Bruckner renormalized one-body interaction and obtain ground-state energies with an accuracy of 0.001 a.u./electron across a wide range of density regimes. Our scheme is particularly useful in the low-density and strongly correlated regimes, where regular CCD has serious drawbacks. Moreover, we cure the infamous overcorrelation of approaches based on ring diagrams (i.e., the particle-hole random phase approximation). Our energies are further shown to have appropriate basis set and thermodynamic limit convergence, and overall this scheme promises energetic properties for realistic periodic and extended systems which existing methods do not possess.
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    Sign problem in full configuration interaction quantum Monte Carlo: Linear and sublinear representation regimes for the exact wave function
    (American Physical Society, 2014) Shepherd, James J.; Scuseria, Gustavo E.; Spencer, James S.
    We investigate the sign problem for full configuration interaction quantum Monte Carlo (FCIQMC), a stochastic algorithm for finding the ground-state solution of the Schrödinger equation with substantially reduced computational cost compared with exact diagonalization. We find k-space Hubbard models for which the solution is yielded with storage that grows sublinearly in the size of the many-body Hilbert space, in spite of using a wave function that is simply a linear combination of states. The FCIQMC algorithm is able to find this sublinear scaling regime without bias and with only a choice of the Hamiltonian basis. By means of a demonstration we solve for the energy of a 70-site half-filled system (with a space of 1038 determinants) in 250 core hours, substantially quicker than the ∼1036 core hours that would be required by exact diagonalization. This is the largest space that has been sampled in an unbiased fashion. The challenge for the recently developed FCIQMC method is made clear: Expand the sublinear scaling regime while retaining exact-on-average accuracy. We comment upon the relationship between this and the scaling law previously observed in the initiator adaptation (i-FCIQMC). We argue that our results change the landscape for the development of FCIQMC and related methods.