Probing quantum phase transition with spread complexity

   The notion of Krylov complexity is an effective measure of operator
   growth, that quantifies the evolution of a simple operator under a given
   Hamiltonian. In this talk, I will discuss how the Krylov basis construction
   generated by the Hamiltonian can be used to describe the spread complexity
   of preparing a target state starting from a given reference state. Then I
   will discuss the geometric approach of extracting the Lanczos coefficients
   under a quantum quench, which are essential for calculating the complexity.
   Finally, I will explain our recent work on using the spread complexity as an
   efficient marker of ground state quantum phase transition.