When one uses tensor network as a wave function ansatz for a variational method, we usually use this scheme to find a ground state. Why can’t we apply the tensor network formalism to find any excited states?

  • $\begingroup$ variational methods are good at finding ground states, and it is more difficult to find excited states. I am not an expert on tensor networks but if the principal idea is variational, I would guess that this is the reason. If you'd like I can explain in an answer why is that so $\endgroup$
    – user245141
    Feb 12, 2020 at 12:05
  • $\begingroup$ I would also like to add that excitations are definitely doable using tensor networks methods, e.g. the "quasiparticle excitation ansatz" (see section 6 of arxiv.org/abs/1810.07006 and numerous other papers) $\endgroup$
    – NDewolf
    Feb 12, 2020 at 12:44
  • 2
    $\begingroup$ The most common tensor network ansatz used (e.g. MPS and PEPS) describe states with area law entanglement. This is the correct entanglement structure for low lying states in a wide range of cases, but not suitable for higher energy states, which generally show volume law entanglement $\endgroup$ Feb 12, 2020 at 12:48
  • $\begingroup$ @yu-v Could you explain why is that so? $\endgroup$ Feb 12, 2020 at 13:11
  • $\begingroup$ @NDewolf Thanks for sharing the article! I haven’t aware of this. I skimmed the section. Is this like magnons in quantum many body system? Is this procedure artificial for true excited particles? not quasiparticles $\endgroup$ Feb 12, 2020 at 13:15


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