# Dresden 2017 – wissenschaftliches Programm

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# O: Fachverband Oberflächenphysik

## O 6: Electronic Structure Theory: New Concepts and Developments in Density Functional Theory and Beyond - I

### O 6.9: Vortrag

### Montag, 20. März 2017, 12:30–12:45, GER 38

**Implementation of the SU(2) Symmetry in FCIQMC using the Graphical Unitary Group Approach** — •Werner Dobrautz^{1} and Ali Alavi^{1,2} — ^{1}Max-Planck-Institut für Festkörperforschung — ^{2}Department of Chemistry, University of Cambridge

The Full Configuration Interaction Quantum Monte Carlo (FCIQMC) algorithm [1] is a projector QMC method, previously formulated in the total anti-symmetric space of Slater Determinants, based on the imaginary-time Schrödinger equation to obtain the ground state of a system in the long-time limit.

By formulating the method in eigenfunctions of the Ŝ^{2} spin-operator via the Graphical Unitary Group Approach [2] we can make use of the block-diagonal form of spin-preserving, non-relativistic Hamiltonians for different values of the total spin. This allows us to lift possible near degeneracies of low-lying excitations of different spin sectors, calculate spin-gaps more easily and obtain the physical correct ground-state, without spin-contamination, and identify its total spin quantum number.

Our method does not rely on expanding the spin-eigenfunctions in linear combinations of Slater Determinants and thus does not hit an exponential bottle neck and can be applied to system sizes larger than previously reachable with similar approaches.

[1] G. Booth, A. Thom and A. Alavi, J. Chem. Phys. **131**, 054106 (2009)

[2] I. Shavitt, Int. J. Quantum Chem. Symp., **11:** 131 (1977); Int. J. Quantum Chem. Symp., **12:** 5 (1978)