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shareloqs / MPSDynamics

Tensor network simulations for finite temperature, open quantum system dynamics
https://shareloqs.github.io/MPSDynamics/
GNU General Public License v3.0
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Variational MPO approach for finding NESS #8

Open 4psireal2 opened 2 months ago

4psireal2 commented 2 months ago

Many thanks for this great repo! Is there a possibility to find the non-equilibrium steady state using a variational approach? For reference

tfmlaX commented 2 months ago

Thank you! I know about this variational approach and it looks very interesting - we can look into it. Do you have some experience with this approach?

4psireal2 commented 2 months ago

Yes I do! Its implementation works for my system, the 1D quantum contact process. However, the ground state is the absorbing state and I want to probe NESS of non-zero particle number density instead. The hope was that NESS could be the first excited state but simulations with DMRG1(2) have only returned unphysical solutions. I think the problem could be due to the vectorised MPO ansatz which doesn't fulfill the positivity property of a density matrix. Also the excited states of Lˆ†L are typically different from the eigenstates of L so I wouldn't know how to interpret the result either.

I just thought with the MPS ansatz of your framework for open system, methods for closed system such as DMRG can be recycled.

4psireal2 commented 2 months ago

Some passsing thought:

  1. How does the MPS's bond dimension grow with time using your implementation?
  2. Is there some relation between the state found by long-time imaginary time evolution and the state found by long-time real time evolution? If yes, how?
tfmlaX commented 2 months ago

I just thought with the MPS ansatz of your framework for open system, methods for closed system such as DMRG can be recycled.

This is non-trivial as we don't work at the level of the reduced systems dynamics but time-evolve the full state of the system and its environment. I'll have to take some time to understand a bit more deeply this variational approach to see how (if?) it can be reformulated/connected to what we do.

How does the MPS's bond dimension grow with time using your implementation?

I would say this is model-dependent and I'm not sure that I'm able to give a general answer.

Is there some relation between the state found by long-time imaginary time evolution and the state found by long-time real time evolution? If yes, how?

Very interesting question. Generally speaking, the long-time imaginary time evolution should bring the state towards the zero-temperature ground state; I do not know under which conditions it is the same as the steady state obtained with real time evolution.