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Quantum chaos and thermalization in gapped systems · Around

2010

Quantum chaos and thermalization in gapped systems

Rigol, Marcos, Santos, Lea F.

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We investigate the onset of thermalization and quantum chaos in finite one-dimensional gapped systems of hard-core bosons.

Integrability in these systems is broken by next-nearest-neighbor repulsive interactions, which also generate a superfluid to insulator transition.
By employing full exact diagonalization, we study chaos indicators and few-body observables.
We show that with increasing system size, chaotic behavior is seen over a broader range of parameters and, in particular, deeper into the insulating phase.

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Temperature ( T T ) and energy ( E E ) are related by E = 1 Z Tr { H ^ e − H ^ / k B T } E=\dfrac{1}{Z}\textrm{Tr}\left\{\hat{H}e^{-\hat{H}/{k_{B}T}}\right\} , where Z = Tr { e − H ^ / k B T } Z=\textrm{Tr}\left\{e^{-\hat{H}/{k_{B}T}}\right\} , k B = 1 k_{B}=1

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