Quantum Monte Carlo calculations of BiScO$_{3}$ ferroelectric well-depths

The perovskite (1-x) BiScO$_{3}$-x PbTiO$_{3}$ alloy has been reported as having a large piezoelectric properties.\footnote {R.E. Eitel, {\it et al.}, {\it Jpn. J. Appl. Phys.}, Part 1 {\bf 40},5999 (2001); R.E. Eitel, {\it et al.}, ibid. {\bf 41}, 1 (2002)} Density functional theory (DFT) using local density approximation (LDA) predicts an extraordinarily large ferroelectric well depths (about 1.2 eV) of the end point compound BiScO$_{3}$.\footnote {J. \'{I}\~{n}iquez, D. Vanderbilt, L. Bellaiche, Phys. Rev B {\bf 67}, 224107 (2003)} We perform quantum Monte Carlo calculations on BiScO$_{3}$ to calculate these well depths. In our QMC method,\footnote{S. Zhang, H. Krakauer, Phys. Rev. Lett {\bf 90}, 136401 (2003)} the two-body terms coming from electron-electron interactions are decoupled using a Hubbard- Stratonovich transformation. The ground state is obtained from projection of an initial trial wave function by random walks in Slater determinant space. To control the sign/phase problem, a trial Slater determinant is used, which in our calculations is taken directly from the DFT calculations. We find in the QMC calculation large finite-size effects in the primitive cell, on the order of a few eV. We study these finite-size effects and explore several schemes to reduce them.