JCMS: Entanglement dynamics and eigenstate correlations in strongly disordered systems

by Bikram Pain (International centre for theoretical sciences Bengaluru)

Friday 7 Jun 2024, 10:30 → 12:00 Europe/Stockholm

Albano 3: 6228 - Mega (22 seats) (Albano Building 3)

The many-body localised phase of quantum systems is an unusual dynamical phase wherein the system fails to thermalise and yet, entanglement grows unboundedly albeit very slowly in time. We present a microscopic theory of this ultraslow growth of entanglement in terms of dynamical eigenstate correlations of strongly disordered, interacting quantum systems in the many-body localised regime. These correlations involve sets of four or more eigenstates and hence, go beyond correlations involving pairs of eigenstates which are usually studied in the context of eigenstate thermalisation or lack thereof. We consider the minimal case, namely the second Renyi entropy of entanglement, wherein the correlations involve quartets of four eigenstates. We identify that the dynamics of the entanglement entropy is dominated by the spectral correlations within certain special quartets of eigenstates. We uncover the spatial structure of these special quartets and the ensuing statistics of the spectral correlations amongst the eigenstates therein, which reveals a hierarchy of timescales or equivalently, energy scales. We show that the hierarchy of these timescales along with their non-trivial distributions conspire to produce the logarithmic in time growth of entanglement, characteristic of the many-body localised regime. This microscopic theory therefore provides a much richer perspective on entanglement growth in strongly disordered systems compared to the commonly employed phenomenological approach based on the $\ell$-bit picture.