Published Paper Details:

The Hubbard model plays a critical role in understanding strongly correlated electron systems, quantum phase transitions, and Mott-insulator states. Optical lattices created by intersecting laser beams offer an ideal experimental platform for simulating the Hubbard model with ultracold atoms, providing precise control over the interaction parameters. This study explores phase diagrams, critical points, and quantum fluctuations within the Hubbard model, extending previous studies through advanced numerical methods such as quantum Monte Carlo simulations. This study also examined coherent pairing states and quantum discord. By integrating experimental insights from fermionic transport in optical lattices, this study provides a comprehensive understanding of the application of the Hubbard model. The interplay between electron correlations and quantum phases is crucial for future studies of quantum materials, emphasizing the utility of optical lattices in validating theoretical predictions.