# Software for solving quantum spin Hamiltonians in 1D and 2D

I'm looking to solve quantum spin Hamiltonians in 1D and 2D (e.g. Heisenberg Model) consisting of a large number of spin sites.

What are the pros and cons of each package, and which package is more suitable for what type of calculations?

Many beginners will be benefit from the answers, and any help in this direction will be appreciated.

Answers in the format of these examples would be appreciated:

• Welcome to the site! Thank you for contributing your question here (+1!) and we hope to see much more of you! It is strongly preferred that one question is asked per post, so the part where you asked specifically about software for "magnetic properties such as magnetization, correlation, susceptibility" can possibly be asked separately, and you can easily get back what you wrote by looking at the edit history. See the examples I provided above, to see what we hope for the questions and answers to look like. Welcome again! Dec 16 '20 at 5:37
• @NikeDattani, Thanks for edit!
– 2.1
Dec 16 '20 at 5:57
• why did you want to close this question (and to rename it)? Oct 7 at 19:46
• @NikeDattani, Didn't get the expected answer, so I am thinking of deleting or modifying it for asking a more precise question.
– 2.1
Oct 17 at 4:12

Note: This answer was written when the question was specifically about exact diagonalization codes. In an ED context, "a large number of spin sites" would maybe mean somewhere in the 24-40 range (maybe slightly more if really pushing the envelope, fewer for $$t-J$$ and Hubbard models) since the Hilbert space grows exponentially. If one is looking to solve problems with larger numbers of sites than that, it's better to look to other computational methods like DMRG or QMC.

## QuSpin

QuSpin is an open-source Python code that can do exact diagonalization of spin, fermion, and boson systems. It has a wide support for use of symmetries, constrained Hilbert spaces, various models, and time evolution. The combination of fairly simple Python syntax and a large number of tutorials make it a great choice for beginners, for small-scale experimentation, and time-evolution problems in many-body systems. However, the parallelization options are limited. As far as I know, as of v. 0.3.6 QuSpin only supports on-node parallelization through OpenMP and MKL. Thus QuSpin is typically not the best choice if you want to reach the largest systems. In addition, QuSpin seems to currently lack built-in support for dynamical correlation functions, which is of interest to modeling inelastic experiments.

References

• Thanks for writing, Yes, It is one option for a beginner to start with
– 2.1
Dec 18 '20 at 6:04
• @Chumbak No problem. I guess I will give others more time to write answers of their own, but if nobody chimes in I could post an answer about HPhi too. Dec 18 '20 at 16:11
• Yeah, Sure, Thanks
– 2.1
Dec 18 '20 at 19:31