Multifractality Meets Entanglement: Relation for Non-Ergodic Extended States

It is now well established that entanglement plays a central role on the thermalization process of quantum many-body systems. On the other hand, ergodicity is deeply connected to the notion of chaos, which also implies the equipartition of the wave function over the available many-body Fock states, which is usually quantified by multi-fractal analysis.

In this talk, I will discuss a link between ergodic properties extracted from entanglement entropy and the ones from the multi-fractal analysis [1]. I will show a generalization of the work of Don. N. Page [2] for the entanglement entropy, to the case of non-ergodic but extended (NEE), states. By implementing the NEE states with a new and simple class of random states, which live in a fractal of the Fock space, I will compute, analytically and numerically, its von Neumann/Renyi entropy. Remarkably, I will show that the entanglement entropies can still present a fully ergodic behavior, even though the wave function lives in a vanishing ratio of the full Hilbert space in the thermodynamic limit.

[1] Phys. Rev. Lett. 124, 200602 (2020)

[2] Phys. Rev. Lett. 71, 1291 (1993)