Alladi Ramakrishnan Hall

Chaos and Krylov Complexity in Bose-Hubbard Model

Debodirna Ghosh

IMSc

In this talk, I will discuss Krylov complexity as an indicator of quantum chaos for a one-dimensional Bosonic system, the celebrated Bose-Hubbard Model. The Bose-Hubbard Hamiltonian consists of interacting bosons on a lattice, describing ultra-cold atoms. Apart from showing superfluid-Mott insulator phase transition, the model also exhibits both chaotic and integrable (mixed) dynamics depending on the value of the interaction parameter. I will focus on the three-site Bose Hubbard Model (with different particle numbers), which is known to be highly mixed (both integrable and chaotic). Using the Lanczos algorithm and finding the Krylov complexity, I will argue that the three-site Bose-Hubbard model exhibits chaotic nature at appropriate limits.