TNT Library : Tensor Manipulation and Storage

Tensor Network Theory (TNT) provides efficient and highly accurate algorithms for the simulation of strongly correlated quantum systems. The corresponding numerical algorithms enable approximate descriptions of many-body states and linear operators acting on them that do not grow exponentially with system size, in contrast to exact descriptions. Whilst TNT algorithms are efficient, they are numerically demanding and require high-performance optimised and parallelised implementations. A TNT library is currently being developed at the University of Oxford to allow users to have access to the complex algorithms needed to solve these problems from their own high level codes. This project is concerned with optimising and parallelising those parts of the TNT library that involve heavy computations, to enable important quantum effects in many-body systems to be studied. The initial objectives were: Obj. 1 Improving storage of the matrices by a more efficient usage of memory and parallelisation using OpenMP. Obj. 2 Developing more efficient and scalable calculations for the core functions of the TNT algorithms which are the most computationally demanding parts. This will mainly concern the contraction and SVD operations. Obj. 3 Improvements in the performance of the code will be achieved by incorporating symmetry information that will allow a decomposition of the tensors into sub-blocks so that they may then be assigned to individual MPI processes.