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I am a condensed matter theorist and I mostly use quantum Monte Carlo methods. I use models like the Heisenberg model, an represent an extreme simplification of real materials to just localized spin degrees of freedom (no electrons, orbitals, etc).

The advantage of this extreme simplification is it allows much more precise studies of the underlying physics. The disadvantage is that it can be difficult to make direct connections to experiments.

I know very little about how ab initio methods work and even less about how they treat magnetism. I would like to have a better sense of the capabilities of these methods.

  1. Is it possible to model strong magnetic correlations or magnetic phase transitions?
  2. Can ab initio methods be used to calculate exchange parameters (like the Heisenberg $J$)?
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    $\begingroup$ Spin-spin can be treated an-initio (Boris Minaev did it for Li$_2$). External magnetic fields can certainly be included. Heisenberg's J can be estimated I believe (see the most cited paper by Steve Winter). I'm sure they can be used to study magnetic phase transitions but I don't know any examples. However I don't know how to answer #3: I only ever calculated spin-orbit interactions, and they tend to be hard, but I lack experience with others so I can't compare 😂 $\endgroup$ – Nike Dattani May 26 at 13:24
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    $\begingroup$ Just a piece of general advice: asking 5 questions at the same time is not the best idea. The question is already extremely broad (what methods? what systems? how do you deal with spin-orbit coupling? etc), maybe you one to focus on one main question of it. $\endgroup$ – Greg May 27 at 10:41
  • $\begingroup$ That's fair, I'll edit it to make it simpler. $\endgroup$ – taciteloquence May 27 at 10:44
  • $\begingroup$ Thank you for the clarification. I have one more question: what do you mean that it is difficult to make a connection with experiments? You mean you have to know J, D etc to have good simulation? Experiments generally give thermal expectation values of different properties, not J such. Ab initio methods in that sense are even harder t compare to experiments as they give only energies of different spin-configurations, you still have to make a thermodynamic model on the top of it, calculate thermal occupations etc. $\endgroup$ – Greg May 28 at 3:02
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    $\begingroup$ To connect to experiments you have to make guesses at J, D, etc, but more importantly, you have to know what the interactions look like in the first place. Are the spins localized? How do they interact with their neighbors and next nearest neighbors, etc? Are those interactions isotropic, etc? If there are any moving electrons or holes (or any interactions that don't involve spin), then accounting for those can be very difficult. $\endgroup$ – taciteloquence May 28 at 3:23
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It is an example where representative of different fields would give you very different answers. I do not want to pretend my answer would be by anyway complete. Short answer: yes. And the devil, as always, is in the details.

  • Since we can solve Schrodinger and Dirac equations arbitrary accuracy (see eg Nakatsuji's work, http://qcri.or.jp/~nakatsuji/nakatsuji.htm), technically speaking we can solve any quantum mechanical problem if we have enough computational power, so it is a YES. The question is always what accuracy and what cost...

  • OK, I guess you meant for systems comparable to the size of the model you run. Then most probably NO.

  • You are asking about strong magnetic correlation and magnetic phase transitions. This is far from my field, but it sounds more like a statistical mechanical problem, not a quantum mechanical problem. But I leave this to others.

  • What can we solve? You are asking about e.g J, J is not an observable but a model parameter in your model. What ab initio and DFT methods can calculate (estimate) is the energy of different spin configurations, and then you can fit it with whatever assumption about the spin-Hamiltonian you want. In the molecular field, it is fairly common in the last decade(s?) to estimate magnetic coupling between metal ions e.g. in catalysts or metalloenzyme active centers. Even methods like DFT can be used to calculate J (through broken symmetry approach) leading to surprisingly accurate results for many systems. Packages like Orca even have keywords to create broken symmetry wavefunctions. If you want more accurate methods, you need something that represents better the multireference character of different spin configurations (eg CASSCF, CASPT2, MR-SAC), but the basic idea is the same. The problem with these methods that they generally scale horribly with the size of the spin system.

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