# Strange behaviour of eigensystem

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

SetDirectory[NotebookDirectory[]]
evv = Get["H.m"];
index=164
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

index=165


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.

• 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? – xzczd Sep 12 '20 at 7:58
• 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. – Rasoul-Ghadimi Sep 12 '20 at 10:46
• 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. – xzczd Sep 12 '20 at 10:50
• @xzczd, please look at youtu.be/JU6-rI5t8-I – Rasoul-Ghadimi Sep 17 '20 at 7:02
• Hmm… strange. Have you contacted WRI support? – xzczd Sep 17 '20 at 7:13