  Although Boron nitride (BN) is a well-known compound widely used for
engineering and scientific purposes, the phase stability of its polymorphs, one
of its most fundamental properties, is still under debate. The ab initio
determination of the ground state of the BN polymorphs, such as hexagonal and
zinc-blende, is difficult because of the elusive Van der Waals interaction,
which plays a decisive role in some of the polymorphs, making quantitative
prediction highly challenging. Hence, despite multiple theoretical studies,
there has been no consensus on the ground state yet, primarily due to
contradicting reports. In this study, we apply a state-of-the-art ab initio
framework - fixed-node diffusion Monte Carlo (FNDMC), to four well known BN
polymorphs, namely hexagonal, rhombohedral, wurtzite, and zinc-blende BNs. Our
FNDMC calculations show that hBN is thermodynamically the most stable among the
four polymorphs at 0 K as well as at 300K. This result agrees with the
experimental data of Corrigan~{\it et al.} and Fukunaga. The conclusions are
consistent with those obtained using other high-level methods, such as coupled
cluster. We demonstrate that the FNDMC is a powerful method to address
polymorphs that exhibit bonds of various forms. It also provides valuable
information, like reliable reference energies, when reliable experimental data
are missing or difficult to access. Our findings should promote the application
of FNDMC for other van der Waals materials.
