Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Eigenstate thermalization hypothesis and eigenstate-to-eigenstate
  fluctuations   We investigate the extent to which the eigenstate thermalization
hypothesis~(ETH) is valid or violated in the non-integrable and the integrable
spin-$1/2$ XXZ chain. We perform the energy-resolved analysis of the
statistical properties of matrix elements $\{O_{\gamma\alpha}\}$ of an
observable $\hat{O}$ in the energy eigenstate basis. The Hilbert space is
coarse-grained into energy shells of width $\Delta_E$, with which one can
define a block submatrix $\tilde{O}^{(b,a)}$ consisting of elements between
eigenstates in the $a$th and $b$th shells. Each block submatrix is
characterized by constant values of $E_{\gamma\alpha}=(E_\gamma+E_\alpha)/2
\simeq \tilde{E}$ and $\omega_{\gamma\alpha}= (E_\gamma-E_\alpha) \simeq
\omega$ up to $\Delta_E$. We will show that all matrix elements within a block
are statistically equivalent to each other in the non-integrable case. Their
distribution is characterized by $\bar{E}$ and $\omega$, and follows the
prediction of the ETH. In stark contrast, eigenstate-to-eigenstate fluctuations
persist in the integrable case. Consequently, matrix elements
$O_{\gamma\alpha}$ cannot be characterized by the energy parameters
$E_{\gamma\alpha}$ and $\omega_{\gamma\alpha}$ only. Our result explains the
origin for the breakdown of the fluctuation dissipation theorem in the
integrable system. The eigenstate-to-eigenstate fluctuations sheds a new light
on the meaning of the ETH.

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The categories of this paper are: stat
35
The categories of this paper are: mtrl-th
26
The categories of this paper are: bayes-an
15
The categories of this paper are: nucl-ex
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The categories of this paper are: patt-sol
3
The categories of this paper are: physics
1
The categories of this paper are: cs
13
The categories of this paper are: quant-ph
7
The categories of this paper are: hep-th
36
The categories of this paper are: cmp-lg
28
The categories of this paper are: alg-geom
22
The categories of this paper are: chao-dyn
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The categories of this paper are: hep-lat
17
The categories of this paper are: q-fin
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The categories of this paper are: funct-an
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The categories of this paper are: atom-ph