Increasing Computational Efficiency for Numerical Solutions to Quantum Many-Body Systems

This talk will give an overview to different methods we are exploring for increasing our ability to compute numerics for the 1-D Heisenberg Ferromagnet spin ring and similar quantum many-body systems. While we have analytical results proving a "turn-around" in energy due to a singlet in the single mode-approximation, historically there has been a lack of numerical results to back these sort of results. In literature at the moment, the largest explored systems have been up to L = 20 sites, with the classical Lancsoz method requiring the assembly and then decomposition of a 10^20 Hamiltonian, assembled as per the corresponding models (mainly XXZ in the case of this presentation). We offer an overview of our current computational efforts using memory-safe and -efficient techniques such as using Rust and matrix decomposition on the Hamiltonian via the hashing method by Lin 1990. This is ongoing work, and such other aspects might be included as they become relevant.