In quantum chemistry, coupled-cluster methods, especially CCSD(T), with complete basis set extrapolation are often considered a "gold-standard" for closed-shell molecules. This means that we consider them as accurate as experimental results. While there are some debates about whether if we should consider them gold-standards, that is beside the point.

My question is if there is any similar method when we study periodic (1D-3D) materials? Should we \ can we consider eg quantum MC methods such?

Edit: As it was pointed out in the comments, different properties require different methods, scale, etc. For simplicity I would like to limit the question to ground state energy.

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    $\begingroup$ That's a good question! Coupled Cluster has only recently entered materials modeling (by the groups of Garnet Chan and Andreas Gruneis, for example). Coupled Cluster is still too expensive for most materials modeling applications, so DFT is still used. Perhaps Quantum Monte Carlo is what people use for benchmarks? Super expensive, but can give the accuracy needed for benchmarks. $\endgroup$ – Nike Dattani May 1 at 4:12
  • $\begingroup$ @NikeDattani I wonder about the differences between the studied materials, as a factor to consider. In molecular sciences, closed-shell large bandgap materials with relatively localized orbitals and light elements are the subject of most studies and benchmarks. In materials science, different spin structures and heavy elements, small bandgaps, etc are much more common. Also, studied properties and accuracy of the measured values can be drastically different. $\endgroup$ – Greg May 1 at 4:51
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    $\begingroup$ Since the properties of materials depends a lot on the scale of the material, we may not have one method to provide the gold standard answer, right? For instance, to study fracture of materials, we may not be doing complete justice by only considering atomistic modelling of materials. So, can there ever be a gold standard? $\endgroup$ – Mythreyi May 1 at 12:28
  • $\begingroup$ I'd agree with @Mythreyi - it depends a lot on the property. For band gaps, etc. something like GW or BSE approaches to density functional are great. For fracture or mechanical properties, I'm not sure they help. $\endgroup$ – Geoff Hutchison May 1 at 16:17
  • $\begingroup$ @Mythreyi Good point. Such a question makes only sense if we specify the properties. $\endgroup$ – Greg May 1 at 18:09

I think the answer is probably: yes, but not just one. Or no, if you want to be very strict.

Depending on the type of system you are studying, different methods may work better or worse and it may not always be obvious why. There is probably not one method that will work best generically.

For quantum spin systems in $d\geq 2$ (lattice Hamiltonians with interactions of the form $\vec S_i \cdot \vec S_j$), the gold standard is quantum Monte Carlo (QMC), with the specific method depending on the specific nature of the material, question. For example, if you wanted to know the transition temperature for the AFM ground state for a 3D Heisenberg model, the gold standard would be Stochastic Series Expansion QMC (SSE) see arXiv.

For lattice Hamiltonians in 1D, the gold standard is matrix product state methods, like DMRG.

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    $\begingroup$ This answer would benefit from some small examples of problems that have a gold standard. $\endgroup$ – Tyberius May 7 at 0:35
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    $\begingroup$ I agree that it would be a better answer if you either give a specific example or at least typical categories where should one expect different methods succeeding, so other answers can elaborate on them. Also, if we cannot predict a method working better or worse in given scenarios, I would definitely not call them any kind of standard. The whole point is to find methods that can be used under well-defined circumstances as a reference to compare other, less reliable but hopefully faster methods. $\endgroup$ – Greg May 7 at 4:07

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