YASTN: Yet another symmetric tensor networks; A Python library for abelian symmetric tensor network calculations

We present an open-source tensor network Python library for quantum many-body simulations. At its core is an abelian-symmetric tensor, implemented as a sparse block structure managed by logical layer on top of dense multi-dimensional array backend. This serves as the basis for higher-level tensor networks algorithms, operating on matrix product states and projected entangled pair states, implemented here. Using appropriate backend, such as PyTorch, gives direct access to automatic differentiation (AD) for cost-function gradient calculations and execution on GPUs or other supported accelerators. We show the library performance in simulations with infinite projected entangled-pair states, such as finding the ground states with AD, or simulating thermal states of the Hubbard model via imaginary time evolution. We quantify sources of performance gains in those challenging examples allowed by utilizing symmetries.