Eigenstate thermalization hypothesis beyond standard indicators: Emergence of random-matrix behavior at small frequencies.

  title={Eigenstate thermalization hypothesis beyond standard indicators: Emergence of random-matrix behavior at small frequencies.},
  author={Jonas Richter and Anatoly Dymarsky and Robin Steinigeweg and Jochen Gemmer},
  journal={Physical review. E},
  volume={102 4-1},
Using numerical exact diagonalization, we study matrix elements of a local spin operator in the eigenbasis of two different nonintegrable quantum spin chains. Our emphasis is on the question to what extent local operators can be represented as random matrices and, in particular, to what extent matrix elements can be considered as uncorrelated. As a main result, we show that the eigenvalue distribution of band submatrices at a fixed energy density is a sensitive probe of the correlations between… 
Eigenstate thermalization hypothesis and eigenstate-to-eigenstate fluctuations.
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Speck of chaos
It has been shown that a local perturbation applied to a single site of the one-dimensional XXZ model is enough to bring this interacting integrable spin-1/2 system to the chaotic regime. Here, we
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Bounds on Chaos from the Eigenstate Thermalization Hypothesis.
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Exponential damping induced by random and realistic perturbations.
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