non-Hermitian Hamitonian for Quantum Trajectory

How do I use this algorithm? What does that parameter do?
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zhaozhang
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Joined: 24 Mar 2023, 14:29

non-Hermitian Hamitonian for Quantum Trajectory

Post by zhaozhang »

I would like to simulate time evolution under a non-Hermitian Hamiltonian with TEBD method for quantum trajectory. However, according to this page: https://github.com/tenpy/tenpy/issues/96 , it is not possible to do TEBD with non-Hermitian Hamiltonian in the very early version. Is it fixed now?
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Johannes
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Re: non-Hermitian Hamitonian for Quantum Trajectory

Post by Johannes »

What exactly do you want to do here? Do you "just" want a non-hermitian H, but still evolve according to the usual Schrödinger equation \(i \hbar \partial_t\vert\psi\rangle = H \vert\psi\rangle\), or do you e.g. also want to apply jump operators or have a Lindblad-style evolution?

That issue you reference is closed in the sense that TEBD should indeed work if your H_bond terms are non-hermitian.
So yes, if you model just has some terms which are non-hermitian, at least TEBD should work correctly.

That being said, it's definitely not the main use case, and let me warn you that other algorithms like the ExpMPOTimeEvolution or TDVP won't work, as they implicitly assume that H is hermitian (e.g. TDVP by using LanczosEvolution rather than the general Arnoldi you'd need for non-hermitian H).

Whatever you try out, I'd highly recommend to make sure everything works as it should by reproducing/comparing to known results for simple examples first.
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