Global Phase Control in TDVP During State Evolution

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?

Thank you!

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.)

Thanks miles for your detailed explanation!

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