  One of the most important and commonly used operations in many linear algebra
functions is matrix-matrix multiplication (GEMM), which is also a key component
in obtaining high performance of many scientific codes. It is a computationally
intensive function requiring $O(n^3)$ operations, and its high computational
intensity makes it well-suited to be significantly accelerated with GPUs.
Today, many research problems require solving a very large number of relatively
small GEMM operations that cannot utilise the entire GPU. To overcome this
bottleneck, special functions have been developed that pack several GEMM
operations into one and then compute them simultaneously on a GPU, which is
called a batch operation. In this research work, we have proposed a different
approach based on linking multiple GEMM operations to MPI ranks and then
binding multiple MPI ranks to a single GPU. To increase GPU utilisation, more
MPI ranks (i.e. GEMM operations) are added. We implement and test this approach
in the field of theoretical physics to compute entanglement properties through
simulated annealing Monte Carlo simulation of quantum spin chains. For the
specific use case, we were able to simulate a much larger spin system and
achieve a speed-up of up to $35\times$ compared to the parallel CPU-only
version.
