Multifractality meets entanglement: relation for non-ergodic extended states

Speaker: Giuseppe De Tomasi, Cambridge University

When: December 18, 2020 (Fri), 12:00PM to 01:00PM (add to my calendar)

This event is part of the Biophysics/Condensed Matter Seminar Series.

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 implies also an 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 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, both 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.

In the final part of the talk, I will apply the aforementioned results to analyze the breakdown of thermalization in kinematically constrained models having Fock/Hilbert space fragmentation [3].

References:

[1] Phys. Rev. Lett. 124, 200602 (2020) [2] Phys. Rev. Lett. 71, 1291 (1993) [3] Phys. Rev. B 100, 214313 (2019)

https://bostonu.zoom.us/j/98731662171?pwd=VGVvSEZLZUlRa0xNbUgvWGh6THA3Zz09