Alexander Haywood

My research investigates the emergence of exotic quantum phases in strongly correlated 1D and 2D systems. I focus on how discrete symmetries, such as exponential and dipole symmetries, generate topological and fractionalized states that resist thermalization. A central component of my work is Hilbert space fragmentation, a phenomenon where a system's internal structure prevents the decay of quantum information, offering a promising path toward robust quantum memory.

To explore these dynamics, I employ numerical techniques including Exact Diagonalization (ED) and the Density Matrix Renormalization Group (DMRG). Because the exponential scaling of many-body systems typically renders 2D models inaccessible, my approach embeds these discrete symmetries directly into the numerical architecture. By decomposing the Hilbert space into isolated symmetry sectors, I can rigorously simulate strongly interacting models that were previously beyond reach. This framework not only unlocks new regimes of many-body physics but establishes the theoretical foundation for the next generation of quantum materials and fault-tolerant hardware.