Many-body localization and delocalization dynamics in the thermodynamic limit

TL;DR

This paper demonstrates that Numerical Linked Cluster Expansions (NLCE) effectively analyze many-body localization (MBL) and delocalization in disordered quantum systems directly in the thermodynamic limit, revealing new insights into spin dynamics under disorder.

Contribution

The study introduces NLCE combined with real-time evolution as a powerful method to investigate MBL in disordered spin and fermionic systems, overcoming finite-size limitations of traditional simulations.

Findings

NLCE outperforms finite-size simulations in capturing long-time dynamics.

Spin remains delocalized in strongly disordered Hubbard chains without tilt.

Tilted potentials induce nonergodic behavior and slow spin imbalance decay.

Abstract

Disordered quantum systems undergoing a many-body localization (MBL) transition fail to reach thermal equilibrium under their own dynamics. Distinguishing between asymptotically localized or delocalized dynamics based on numerical results is however nontrivial due to finite-size effects. Numerical linked cluster expansions (NLCE) provide a means to tackle quantum systems directly in the thermodynamic limit, but are challenging for models without translational invariance. Here, we demonstrate that NLCE provide a powerful tool to explore MBL by simulating quench dynamics in disordered spin-$1/2$ two-leg ladders and Fermi-Hubbard chains. Combining NLCE with an efficient real-time evolution of pure states, we obtain converged results for the decay of the imbalance on long time scales and show that, especially for intermediate disorder below the putative MBL transition, NLCE outperform direct simulations of finite systems with open or periodic boundaries. Furthermore, while spin is delocalized even in strongly disordered Hubbard chains with frozen charge, we unveil that an additional tilted potential leads to a drastic slowdown of the spin imbalance and nonergodic behavior on accessible times. Our work sheds light on MBL in systems beyond the well-studied disordered Heisenberg chain and emphasizes the usefulness of NLCE for this purpose.