Alladi Ramakrishnan Hall

Growth of number entropy and dephasing induced relaxation in strongly disordered systems

Roopayan Ghosh

University College London (UCL)

In this talk I will discuss about two aspects of localized systems.

First, I would discuss the recently discovered slow growth of number entropy in many-body localized systems, which in the thermodynamic limit is said to herald the eventual onset of delocalization. By numerically studying number entropy in the disordered isotropic Heisenberg model we first reconfirm that, indeed, there is a small growth. However, we show that such growth is fully compatible with localization. To be specific, using a simple model that accounts for expected rare resonances we can analytically predict several main features of numerically obtained number entropy: trivial initial growth at short times, a slow power-law growth at intermediate times, and the scaling of the saturation value of number entropy with the disorder strength.

Second, I will talk about the relaxation of observables to their nonequilibrium steady states in a disordered XX chain subjected to dephasing at every site. Localization is said to preserve coherence in the system and it is imperative to understand, specially from experimental point of view, the proper timescales when such a system is undergoing decoherence. We comprehensively analyze the relaxation of staggered magnetization, i.e., imbalance, in such a system, starting from the Néel initial state. We analytically predict the emergence of several timescales in the system and show that an often reported stretched exponential decay is just one of the regimes which holds in a finite window of time. Subsequently, the asymptotic decay of imbalance is governed by a power law irrespective of the disorder. The continuum limit of the low magnitude eigenspectrum of the Liouvillian is key to this understanding.



References:-

Roopayan Ghosh and Marko Žnidarič, Phys. Rev. B 105, 144203 – Published 13 April 2022
Roopayan Ghosh and Marko Žnidarič Phys. Rev. B 107, 184303 – Published 4 May 2023.