First, get yourself a way to take notes. You should be able to look at the paper and your notes at the same time. That could be using a large screen with a text file, or it could be good old pen and paper. You will want to write down the answers to the questions below as well as any words that you don’t know. Look up those words. If you are new to reading papers, expect it to take you a long time to understand a paper. If you are not new to reading papers you already know this.
For the sake of an example, let’s go through a paper from our group: https://arxiv.org/abs/2009.13556
Why did they do what they did?
The answer to this question is typically in the abstract and beginning of the introduction. There will generally be two goals/objectives:
The large goal in the field. The paper will not typically answer this question. For our example paper, we find this in the first paragraph. We want to develop scalable methods to access excited states, for the even larger goal of understanding correlated electronic states.
The specific goal of the paper. The specific goal of this paper is to explain and assess an algorithm to compute excited states in variational Monte Carlo using a penalty method.
The purpose of the introduction is to explain why the specific question is important in the context of the larger goal. In the example above, the paper summarizes other attempts to use variational Monte Carlo, and what gaps there are in those previous attempts that prevent us from achieving the larger goal.
What did they actually do?
Figure out what was actually done in the study. At this point, don’t try to interpret what anything means. Just determine what was actually done and what the results were. Typically the figures are guides to this. For this paper, I see the following important things:
- The objective function $O[\Psi] = E[\Psi] + \sum_i^N \lambda_i |S_i|^2$ has the N+1’th excited state as its minimum.
- A method optimizing the objective function $O[\Psi]$ enables optimization of orbitals, determinant coefficients, and Jastrow parameters.
- A CASCI-J wave function agrees with full CI for H2, using this method.
- DMC on a CASCI-J wave function, with all parameters optimized agrees with CC3 within around 0.24 eV for benzene. For fixed parameters the difference is 0.35 eV.
Looking back at the paper this way, I note that we could probably have made some of these things clearer. Note that you may have a slightly different list than I have, and that does not necessarily make it wrong.
Did they achieve their original specific goal?
Now we can make a judgement about the paper. Did they achieve their specific goal? The answer here I think is yes; the algorithm is explained in detail along with an implementation available online. It is demonstrated to function efficiently on a case where there are good benchmarks. The algorithm is shown to be capable of optimizing wave functions that at least in principle could describe strong correlation.
What gaps exist between the specific goal and the overall goal?
The calculations were only performed on hydrogen and benzene, fairly simple systems. While some of the excited states are ‘strongly correlated,’ this is still a far cry from demonstrating accurate calculations of excited states on the cuprates, as was mentioned in the introduction. This is ok; a paper does not need to solve the larger goal to be valid.