The Joint Condensed Matter Seminar (JCMS) series is organised by KTH Royal Insitute of Technology, Nordita, and Stockholm University.
On Friday, September 23rd, 2024 from 11 am to 12 am we will host a seminar by Devanshu Shekhar from Indian Institute of Technology.
Entanglement dynamics in system-dependent random matrices: A complexity parameter formulation
The conventional RMT models, the Gaussian Orthogonal Ensembles (GOE) and its cousins are limited to model ergodic systems. Similarly, the Gaussian Wishart Ensembles (GWE) have been well studied to describe ergodic bi-partite states (by ergodic states, we mean that there is a complete delocalization of the state in its Hilbert space). Dynamical models of the RMT, e.g., the Rosenzwig-Porter ensemble (RPE), the power-law banded random matrices (PBRM), etc., have been shown to capture the non-ergodic behaviour of Anderson and many-body localization succinctly. Nevertheless, similar models in the context of non-ergodic states are not known.
Our work introduces models for non-ergodic states whose components are independent but not identically distributed and are inspired by the RPE and the PBRM. Most intriguingly, we show that the seemingly distinct ensembles can be unified under a common mathematical formulation, called the complexity parameter (CP) formulation. Using the CP formulation, we show that a universal evolution pathway for bi-partite entanglement can be achieved. Moreover, we also study the CP formulation for the eigenstate of a many-body Hamiltonian, which is more challenging as the correlation of eigenstate components will now have to be considered. We have applied the formulation to a particular Hamiltonian of immense interest: The random-field Heisenberg model and describe the evolution of the entanglement entropy with the CP. It’s interesting to note that the calculations remain oblivious to any of the system details; the latter enter only through the CP. This implies the calculations can be used to describe a wide range of systems of interest.