Graduate What is best way to start learning DMRG for Fermions?

[Luqman Saleem]

I want to learn the density matrix renormalization group (DMRG) method in traditional formalism (not MPS). While there are many good introductory level articles available for bosonic (and spin) systems, I have not encountered any introductory level article which deals with fermionic systems i.e. Hubbard model and its variants. All articles mention the DMRG algorithm (for the finite and infinite chain) but none of them explicitly explains it for fermionic systems. i.e. how to do half-filling, 3/4 filling e.t.c.

Do you happen to know any introductory level article which explains the technicalities of fermionic DMRG? If there are not any such article, can you please shed some light on the fermionic DMRG.

Thank you so much in advance.

 

[aaroman]

I wanted to add sometime Hubbard chains to my open source DMRG project (described here: https://compphys.go.ro/density-matrix-renormalization-group/ - it's the 'old style', for MPS I have a TEBD project, too) but I don't have enough time for it.

There is a sign issue that complicates things for fermionic operators, that's why the simple implementations and tutorials are avoiding it. You might find the links on my blog helpful, I think I pointed out at least two ways of dealing with the issue - some PhD thesis that deals with Hubbard models and I also pointed the way ITensor deals with it, with the Jordan-Wigner transformation.

 

[Luqman Saleem]

I wanted to add sometime Hubbard chains to my open source DMRG project (described here: https://compphys.go.ro/density-matrix-renormalization-group/ - it's the 'old style', for MPS I have a TEBD project, too) but I don't have enough time for it.

There is a sign issue that complicates things for fermionic operators, that's why the simple implementations and tutorials are avoiding it. You might find the links on my blog helpful, I think I pointed out at least two ways of dealing with the issue - some PhD thesis that deals with Hubbard models and I also pointed the way ITensor deals with it, with the Jordan-Wigner transformation.

First of all, thank you so much for that open source project. I actually started with your work. The PhD thesis that you have mentioned helped me in dealing with the sign problem. I guess, right now I am not able to understand the diagonalization of a Hamiltonian in the subspace of particles. I have explained it in more details here https://www.physicsforums.com/threa...agonalize-a-hamiltonian-in-a-subspace.965747/
I will be very thankful if you could have a look at it and tell me what am I missing.