Hello, I am currently learning how to use itensor to compute open systems. I found that TEBD and TDVP are the methods for time evolution in the itensor, but the lindblad master equation used in my model is dissipative. I want to ask whether TDVP has the ability to evolve master equation.
Yes, the TDVP method can be used to simulate open quantum systems. When I searched the literature for applications of TDVP to these systems I found several papers, for example this one:
https://journals.aps.org/pra/abstract/10.1103/PhysRevA.86.062115
Our TDVP code assumes one is evolving a state by some MPO H as e^{-i H t} \ket{\Psi} however \ket{\Psi} here could be a “purified” density matrix so it could represent an open system.
I really appreciate the detailed replies.
I will read this paper carefully.
Great. There might be papers on this which are more accessible and easier to read, so I’d suggest you look for a few different ones and compare their approaches. Good luck!
That’s works with TDVP or TEBD to propagate your Lindblad master equation but not directly. As the first step, you need to reshape the density matrix equation into wave-like (1d vector) equation, e.g., \hat{a}\hat{\rho}\hat{a}^\dagger to \hat{a}\hat{b} W(t) (Purification or kronecker product) with operator \hat{b} considered as fictitious modes, functioning as counterpart to the operator \hat{a} modes.
Then you can perform the time evolution with TDVP, the reduced dynamics can be obtained by another trace or not.