Quantum transfer of interacting and entangled qubits

Recently it was shown, in the three-dimensional Anderson model [1] and the avalanche model of ergodicity breaking transitions [2], that the spectral form factor and the Thouless time extracted from the spectral form factor are scale invariant quantities at eigenstate transition. Thus they represent useful measures for characterisation of eigenstate transition. In the literature, an alternative definition of the Thouless time was given in terms of survival probability [3,4] which measure the stability of an initial state. Motivated by this fact, we investigate the survival probability measure and possible connections to the spectral form factor measure.

We focus on differences in behavior of the survival probability across the eigenstate transitions. Remarkably, we observe scaling invariant power-law decay of the survival probability at the transition in three physically relevant models: the three-dimensional Anderson model, one-dimensional Aubry-Andre model, and the avalanche model of ergodicity breaking transitions. We discuss connections of this universality to the universality of the spectral form factor measure. Our study [5] demonstrate that both quantities, the survival probability and the spectral form factor, are useful tool for detection of the eigenstate transitions.

[1] J. Šuntajs, T. Prosen and L. Vidmar, Annals of Physics 435, 168469 (2021)

[2] J. Šuntajs and L. Vidmar, Phys. Rev. Lett. 129, 060602 (2022)

[3] M. Schiulaz, E. J. Torres-Herrera, and L. F. Santos, Phys. Rev. B 99, 174313 (2019)

[4] T. L. M. Lezama, E. J. Torres-Herrera, F. Pérez-Bernal, Y. Bar Lev, and L. F. Santos, Phys. Rev. B 104, 085117 (2021)

[5] M. Hopjan and L. Vidmar, ArXiv:2212.13888