Ground state description of BiCu$_2$PO$_6$ and BiCu$_2$AsO$_6$

Low dimensional spin systems have always been of interest to the physics community due to their inherent exotic magnetic properties. A further impetus for the study of low-dimensional spin systems was given by the discovery of spin-ladder materials, due to the fact that they are intermediate objects between 1D and 2D systems. Recent experiments by two groups [1,2] on a spin-ladder material BiCu$_2$PO$_6$ exhibited a gapped singlet ground state with a spin gap of about 34 K, though the strength of the spin-exchange interactions have remained controversial. No consensus has been reached on the correct spin-ladder model to describe this compound. We will report on our re-investigations of BiCu$_2$PO$_6$ and the related material BiCu$_2$AsO$_6$ using density functional theory based electronic structure calculations and as well as Transfer Matrix Renormalization Group (TMRG) calculations. Our results necessitate the inclusion of previously neglected exchange couplings to describe the spin-ladder model more adequately.\\[4pt] [1] B. Koteswararao, {\it et. al.}, Phys. Rev. B {\bf 76}, 052402 (2007).\\[0pt] [2] O. Mentr\'{e}, {\it et. al.}, Phys. Rev. B {\bf 80}, 180413 (2009).