Previously I posted about learning how to critically read experimental papers.
A theory paper may claim
"We can understand property X of material Y by studying effective Hamiltonian A with approximation B and calculating property C."
Again it is as simple as ABC.
1. Effective Hamiltonian A may not be appropriate for material Y.
The effective Hamiltonian could be a Hubbard model or something more "ab initio" or a classical force field in molecular dynamics. It could be the model itself of the parameters in the model that are not appropriate. An important question is if you change the parameters or the model slightly how much do the results change. Another question, is what justification is there for using A? Sometimes there are very solid and careful justifications. Other times there is just folklore.
2. Approximation B may be unreliable, at least in the relevant parameter regime.
Once one has defined an interesting Hamiltonian calculating a measurable observable is usually highly non-trivial. Numerous consistency checks and benchmarking against more reliable (but more complicated and expensive) methods is necessary to have some degree of confidence in results. This is time consuming and not glamorous. The careful and the experienced do this. Others don't.
3. The calculated property C may not be the same as the measured property X.
What is "easy" (o.k. possible or somewhat straightforward) to measure is not necessarily "easy" to calculate and visa versa. For example, measuring the temperature dependence of the electrical resistance is "easier" than calculating it. Calculating the temperature dependence of the chemical potential in a Hubbard model is "easier" than measuring it.
Hence, connecting C and X can be non-trivial.
4. There may be alternative (more mundane) explanations.
The experiment was wrong. Or, a more careful calculation of a simpler model Hamiltonian can describe the experiment.
Theory papers are simpler to understand and critique when they are not as ambitious and more focused than the claim above. For example, if they just claim
"effective Hamiltonian A for material Y can be justified"
"approximation B is reliable for Hamiltonian A in a specific parameter regime"
"property C and X are intricately connected".
Finally, one should consider whether the results are consistent with earlier work. If not, why not?
Can you think of other considerations for critical reading of theoretical papers?
I have tried to keep it simple here.