# Total spin operator for Electron sites system **URL:** \ **Category:** DMRG and Numerical Methods\ **Tags:** julia\ **Created:** [April 24, 2025, 1:48am UTC](https://itensor.discourse.group/t/total-spin-operator-for-electron-sites-system/2358 "2025-04-24T01:48:55Z")\ **Posts on this page:** 1\ **Showing post:** 3
**Author:** ![ryanlevy](https://yyz2.discourse-cdn.com/free1/user_avatar/itensor.discourse.group/ryanlevy/32/150_2.png) [@ryanlevy](https://itensor.discourse.group/u/ryanlevy)\ **Post date:** [April 24, 2025, 12:29pm UTC](https://itensor.discourse.group/t/total-spin-operator-for-electron-sites-system/2358/3 "2025-04-24T12:29:48Z")
To continue Vince’s answer, check out the references here: > [@MPO construction and compression principles (or: how does OpSum work?)](https://itensor.discourse.group/t/mpo-construction-and-compression-principles-or-how-does-opsum-work/1898/2): > > For construction, I would recommend checking out if you haven’t [[0708.1221] Finite automata for caching in matrix product algorithms](https://arxiv.org/abs/0708.1221)[[0804.2509] Infinite size density matrix renormalization group, revisited](https://arxiv.org/abs/0804.2509) And this paper on MPO compression [[1909.06341] Local Matrix Product Operators: Canonical Form, Compression, & Control Theory](https://arxiv.org/abs/1909.06341) I’ll have to let others comment on the exact compression techniques that are in ITensors and Miles has nice notes below: > [@MPO construction and compression principles (or: how does OpSum work?)](https://itensor.discourse.group/t/mpo-construction-and-compression-principles-or-how-does-opsum-work/1898/4): > > This is an interesting topic, for sure, and there has been a lot of theoretical progress on it. The main reference for the system currently used by OpSum is: “Matrix Product Operators, Matrix Product States, and ab initio Density Matrix Renormalization Group algorithms” Chan, Keselman, Nakatani, Li, White [https://arxiv.org/abs/1605.02611](https://arxiv.org/abs/1605.02611). For a brief summary of the construction there, I’m attaching the pdf notes below that I wrote for one of the Flatiron postdocs helping us to generalize tha… * * * > As a follow up question, would you assume that adding such term to the Hamiltonian for a 2x8 system (max.bond dim. ~2000-4000) would still be a feasible calculation? (I guess I’ll just have to try). You can always pass MPOs individually (`dmrg([H1,H2], psi0;...)`, and since this is a low “bond dimension” MPO it should not create too much more work compared your “energy” Hamiltonian --- _[View the full topic](https://itensor.discourse.group/t/total-spin-operator-for-electron-sites-system/2358)._