Hi,
I am working with two different Hamiltonians, H_1 and H_2, evolving two distinct quantum states, ψ_1 and ψ_2, separately using the Time-Dependent Variational Principle (TDVP). Under time evolution, each quantum state accumulates a phase factor based on its respective Hamiltonian. After evolving both states using TDVP, I compute the overlap between the two evolved states at a specific time. The results I obtain are in reasonable agreement with exact calculations.
Does TDVP inherently account for and manage the global phase factor that arises during evolution?
I believe TDVP does inherently account for any global phase factor. More specifically, TDVP computes an approximation to the following state:
|\psi(t)\rangle = e^{- i H t} |\psi(0) \rangle
This is a well-defined state with no ambiguity in terms of any phase factor. The global phase factor you are mentioning may be more of a physics concept than a specific mathematical concept, but I could be wrong about that.
(Note also that our tdvp function in ITensorMPS does not include the -i factor for you and you have to include that yourself in the inputs to tdvp.)