Hi all,
I hope this is okay to ask here, but I didn't know where else to ask it. I've been trying to do a different periodic DMRG algorithm that splits the first site so that it is in both the left and right blocks. This is in trying to do a DMRG algorithm kind of like the matrix product state sort that works so much better. I've been having some problems with doing this and was wondering if anyone had any ideas.
I'm only considering a 1D Heisenberg S=1/2 model for now. First of all, I keep track of the Sz operator of the first site of the left block and the last site of the right block (which are really the same site). I make the superblock hamiltonian and diagonalize within the states that have Sz_total=0 for lowest energy AND Sz of first site of left block equal to the last site of the right block (they should have the same Sz spin since they are essentially the same site). When making the superblock hamiltonian, the Sz terms don't require any special consideration. However, the S_plus/S_minus ones do because when the 1st site of the left block is raised, the last site of the right block must also be raised, but the energy should be that of only raising one site. This is where there are problems. I have tried several ways but been unsuccessful. What must be made is an operator that raises both sites as if they are one. Any ideas out there? Is this possible to do at all? Is it impossible because of the minus sign problem with the electrons? Let me know if I wasn't clear enough. Also, when I rotate the a block after finding the highest eigenvalued eigenvectors of the reduced density matrix, I have to find the eigenvectors that preserve both Sz_total and Sz of the first site (in the case of the left block). I'm thinking that this will make the method less effective, but do you think that this will make the method ineffective?
Thanks for your time and thoughts,
Justin Peel