Research Projects

Quantum complexity has become a crucial tool for understanding quantum chaos in fields like quantum field theory, quantum gravity, and condensed matter physics. Krylov complexity (K-complexity) measures operator size growth in Krylov space, which exhibits universal behavior in quantum chaotic systems. The concept of K-complexity has a specific time evolution profile similar to diffeomorphism-invariant quantities of gravity in Ads space. Researchers aim to investigate the K-complexity of the Complex Double-scaled sachdev-Ye-Kitaev (DssYK) model, a sYK model with complex fermions and a gravity dual in a two-dimensional Ads space. They plan to build up the Krylov basis from the Hilbert basis of fixed chord-number states and find an appropriate charged wormhole solution in the two-dimensional Ads space. They also plan to study the dynamics in the Bose-Hubbard model, which exhibits quantum chaos and the Mott insulator-superfluidity phase for finite chemical potential.