Auxilliary Field Quantum Monte Carlo Calculations of Ferroelectric Instability

The perovskite structure alloys (BiScO$_{3}$)$_{1-x}$ -(PbTiO$_{3}$)$_{x}$ have strong ferroelectric instabilities. The ferroelectric double-well depths of BiScO$_{3}$, calculated by density functional theory (DFT), are an order of magnitude larger than for PbTiO$_{3}$ and PbZrO$_{3}$\footnote{J. \'{I}\~{n}iquez, D. Vanderbilt, L. Bellaiche, {\it Phys. Rev B}{\bf 67}, 224107 (2003)}. We carry out quantum Monte Carlo (QMC) calculations on BiScO$_{3}$ to help assess the accuracy of DFT. We use a recently developed auxilliary field QMC method \footnote{S. Zhang, and H. Krakauer, {\it Phys. Rev. Lett} {\bf 90}, 136401 (2003)}. The two-body electronic Coulomb interactions are decoupled using a Hubbard-Stratonovich transformation. The method iteratively projects out the ground state from an initial trial wave function by random walks in the space of Slater determinants. The trial wave function is a single Slater determinant constructed from a DFT calculation using ABINIT \footnote{http://www.abinit.org}. A plane wave basis and periodic boundary conditions were used in the calculations. The ions are represented by norm-conserving Kleinman-Bylander non-local pseudopotentials. Applications of the method on simpler systems gave very encouraging results.