I encounter with really strange behavior in calculating the eigensystem of a hermitian matrix. I upload the matrix here. After loading it you can construct the main matrix as follows

evv = Get["H.m"];
H = Normal@SparseArray[#[[1]] -> Exp[I index #[[2]]] & /@ evv, {1393,1393}] // # + #\[ConjugateTranspose] &;

Calculating eigenvalue and eigensystems takes just one second,

Eigenvalues[H]; // AbsoluteTiming
Eigensystem[H]; // AbsoluteTiming

However by putting


and reconstructing H and calculating eigenvalues and eigensystem, I realize eigenvalue just takes the same time as index=164, while eigensystem take lots of time, without any results. I try to add a very small number to the index, where I get the answer for 165, but for another index, I encounter the same problem.

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    $\begingroup$ 1. Please don't add bugs tag to the question before it's confirmed. 2. Can't reproduce the mentioned behavior in v12.1.1, Win 10, which version and OS are you in? $\endgroup$ – xzczd Sep 12 '20 at 7:58
  • $\begingroup$ I run it on Mathematica 12 in Linux and windows 10. Have you find eigensystem? I would be thanks anyone find my problem comments here. $\endgroup$ – Rasoul-Ghadimi Sep 12 '20 at 10:46
  • $\begingroup$ Yes, 0.470589 for Eigenvalues[H]; // AbsoluteTiming and 0.833236 for Eigensystem[H]; // AbsoluteTiming on my 2 GHz laptop. Just tested on v12.0.1, still cannot reproduce the problem. $\endgroup$ – xzczd Sep 12 '20 at 10:50
  • $\begingroup$ @xzczd, please look at youtu.be/JU6-rI5t8-I $\endgroup$ – Rasoul-Ghadimi Sep 17 '20 at 7:02
  • $\begingroup$ Hmm… strange. Have you contacted WRI support? $\endgroup$ – xzczd Sep 17 '20 at 7:13

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