Product state results

How do I use this algorithm? What does that parameter do?
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on0001st
Posts: 12
Joined: 27 Aug 2018, 09:30

Product state results

Post by on0001st »

Sometimes when using tenpy DMRG class, the final result produced from the dmrg is a product state. I believe this is the case as all of the bond dimensions are 1. There are times when this is the right result but sometimes it is not too.

I was wondering what is the reason that DMRG converges to this wrong results and what can be done to perturb the system to push it out of this 'local minima'. One possible reason is the initial state being a trivial state to the Hamiltonian, e.g. all spin up or down. What I do is to initialise a "random" state of spin ups and downs and then DMRG can then converge to the correct result. Would this be correct?

There are also other cases when even changing the initial state does not allow proper convergence. What should be done then?
QichengTang
Posts: 32
Joined: 08 Jan 2019, 03:03

Re: Product state results

Post by QichengTang »

I will ask you the question what Johannes asked me: What the "random" state means here?

It should be noticed that the charge (quantum number) should be conserved in dmrg, so if your random state has a different total charge, the result will be wrong.

Perhaps you can use "RandomUnitaryEvolution" to get the state you want.

BTW, it's difficult to answer your question, since you just talk about something very abstract.
on0001st
Posts: 12
Joined: 27 Aug 2018, 09:30

Re: Product state results

Post by on0001st »

Thanks for your reply Qicheng!

I have seen your post and I think what I mean by random here is different from what you needed. I would say the "random" state that I mean here is simply a random product state, i.e., a random sequence of spin ups and downs for spin half as opposed to a initial state of all spin up for example. What I seem to understand from your post is that you required a state obtained randomly in the Hilbert space with finite "random" amount of entanglement in the state.
QichengTang wrote: 27 Feb 2019, 10:07 It should be noticed that the charge (quantum number) should be conserved in dmrg, so if your random state has a different total charge, the result will be wrong.
I was under the impression that this would be a problem if we have the conserve parameter set to true. I would assume that DMRG would be able to obtain the correct ground state result for a ferromagnetic Heisenberg spin chain even when an initial state of total spin = 0 is used.

I was hoping to get some insights into this issue through discussion. It could very well be my lack of understanding that I am facing this issues.
QichengTang
Posts: 32
Joined: 08 Jan 2019, 03:03

Re: Product state results

Post by QichengTang »

I believe it's easy to generate a random product state with a given total charge.
for example, for qubit, it's just a combination of 0 and 1 with a given sum of all elements in the list, you just need to give the number of 0 and 1, and do a random permutation.
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