Massively Parallel Approaches to Frustrated Quantum Magnets

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Thesis overview: Quantum magnets are one of the paradigmatic platforms for the investigation of strongly correlated, highly entangled states of matter. On the experimental side, rapid advances in the field of magnetic materials and cold atoms in optical lattices are nowadays heavily challenging theoretical methods. In parallel, these impressive experimental capabilities are providing novel probing tools that might be used to detect and understand entangled phases without direct access to the system wave function. A key question is thus if, and to which extent, it is possible to utilize these probing tools to theoretically understand highly entangled phases of matter from a perspective based on experimentally available probes. A particularly promising route is the exploration of dynamical structure factors that are experimentally accessible, for instance, in inelastic neutron scattering experiments. An application to simulate the dynamical structure factor with Dynamical Lanczos method is presented in this thesis. The physical system is modeled by 1/2-spins placed in a one-dimensional chain or a two-dimensional square lattice with periodic boundary conditions and with energies governed by a XXZ antiferromagnetic Hamiltonian. No translational invariance is imposed, as disordered systems want to be studied, but conservation of the total magnetization is a restriction enforced to the system. The characteristics of the problem require the use of Exact Diagonalization (ED) technique to search for the eigenstates of the system, approximations are ruled out. This method demands the construction, and usually the storage, of the basis elements and the Hamiltonian matrix, which requires a large amount of memory. This amount increases exponentially with the number of spins present in the system, reaching already tens of terabytes for 38 spins. Moreover, this has a direct effect on the amount of computational resources needed to obtain the eigenstates of the system. The reasons mentioned before demand a High Performance Computing (HPC) approach if the goal is to be as realistic as possible. This is the purpose of this project, and all the efforts were put in making it possible.