Statistical properties of the off-diagonal matrix elements of observables in eigenstates of integrable systems

We study the statistical properties of the off-diagonal matrix elements of observables in the energy eigenstates of integrable quantum systems. They have been found to be dense in the spin-1/2 XXZ chain, while they are sparse in noninteracting systems. We focus on the quasimomentum occupation of hard-core bosons in one dimension and show that the distributions of the off-diagonal matrix elements are well described by generalized Gamma distributions, in both the presence and absence of translational invariance but not in the presence of localization. We also show that the results obtained for the off-diagonal matrix elements of observables in the spin-1/2 XXZ model are well described by a generalized Gamma distribution.

Automated summary

This study investigates the statistical properties of off-diagonal matrix elements of observables in the energy eigenstates of integrable quantum systems. It is found that these matrix elements are dense in the spin-1/2 XXZ chain, while being sparse in noninteracting systems. The distribution of off-diagonal matrix elements in the quasimomentum occupation of hard-core bosons in one dimension is well described by generalized Gamma distributions, irrespective of translational invariance but not in the presence of localization. Additionally, the off-diagonal matrix elements of observables in the spin-1/2 XXZ model can be well described by a generalized Gamma distribution.