[Julia] DMRG simulation for an specific total magnetizagion Sector

Question

Hello ITensors team,

I'm exploring the possibility of study the gap closing behavior at quantum phase transition for an Ferrimagnetic spin system following for example the paper [https://arxiv.org/abs/cond-mat/9905224][1]

For that Hamiltonian described by eq(2) and using the Oshikawa-Yamanaka-Affleck theorem, we know in which total magnetization sector the Plateau-1/2 phase appears.
So my question is, how can we specify in which Magnetization Sector are we performing our DMRG calculation ? I mean, how can we specify an total QN number for an ProductMPS wave function of Sz_total component assuming its conservation ?

Thank you

Answer 1

Hi, yes so this is definitely something you can do with ITensor. The short answer is that if you use site indices which contain quantum number (QN) information and if you initialize your initial product state MPS to have a certain well-defined total Sz, then the MPS will remain in that same Sz sector throughout.

The following tutorial goes over this in more detail with an example:
http://itensor.org/docs.cgi?vers=julia&page=getting_started/qn_dmrg

Best regards,
Miles

Comments

Hi Miles, Thank you for the reply.

Yes i know this tutorial, but whats options Beyond "Up" and "Dn" we can use ?
 If for example i want to calculate the Haldane Gap for spin-1 systems using the gap energies between Sz_tot=1 and Sz_tot=0 ground state energies, how can i specify the Sz_tot=1 for example ?
Or for an ferrimagnetic(1/2,1) with 100 unit cells for example, where the magnetic Plateau-1/2 appears at the magnetization sector Sz_tot = 50. How can we construct that MPS ?

Thank you again !

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Hi, I see thanks for clarifying. I just expanded that example with a new section explaining how to set the state to have other total QN values. The ITensor DMRG code will conserve whichever total QN you initialize your state to have:
http://itensor.org/docs.cgi?vers=julia&page=getting_started/qn_dmrg

So if you want to set a total Sz of +1 (physical units, +2 in ITensor units) for your Haldane S=1 system, just flip one of the spins from being "Dn" to being "Up" in the input state that you use.

For the ferrimagnetic case, just make sure that the total Sz of the state you use adds up to 50.

Best regards,
Miles

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Thank you Miles ,  great expansion on those section. Now is clear how i can do that.