Is DMRG Wrong?

Well, I was pretty cautious in calling something completely wrong. I cannot call ER-EPR “wrong” nor can I say holography is “wrong”… they are just somehow trivial and limited in scope and power. About DMRG I can say pretty confidently that it is wrong. It is an idea based on the fact that there is no intrinsic quantum behavior in electron systems and that one could in principle fit whatever one wants to whatever one choses. It may work ok when the entanglement of ground states is small but whenever entanglement starts being relevant and scales not as a strict area law it becomes utter nonsense. This is why I never follow the DMRG ideas and I don’t go to DMRG conferences or “schools”… Now, if you, as an objective reader of this blog, wants to try DMRG please feel free to do so and read whatever has been written about the subject. You will see, after some effort that in my case was of around 10 minutes for a walk in Palermo with one of the persons that “applied” DMRG to quantum chemistry, that the whole idea is based on unphysical assumptions and it is plain wrong… Nature is not restricted to little or no entanglement and in the end you cannot perfectly factorize the tensors so that the density matrixes are separated completely. This is why the idea works ok-ish for 1 dimensional systems: the area law is there exact. entanglement is “contained” in the “fictive black hole” and interactions are short range… For everything else the situation is fundamentally different (see EPR effects, quantum correlations, etc.) and the idea is useless and pointless…



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