Density-Matrix Renormalization Group study of Many-Body Localization in Floquet Eigenstates

TL;DR

This paper extends the DMRG-X algorithm to efficiently find Floquet eigenstates in periodically driven many-body localized systems, demonstrating the robustness of area-law entanglement scaling in larger systems.

Contribution

The authors generalize the DMRG-X algorithm to Floquet systems using matrix-product operators, enabling analysis of larger systems beyond exact diagonalization.

Findings

Area-law entanglement scaling persists in larger Floquet MBL systems

The generalized DMRG-X accurately reproduces eigenstates compared to exact methods

Floquet eigenstates exhibit robust localization properties

Abstract

We generalize the recently introduced Density-Matrix Renormalization Group (DMRG-X) [Khemani et al, PRL 2016] algorithm to obtain Floquet eigenstates of one-dimensional, periodically driven many-body localized systems. This generalization is made possible by the fact that the time-evolution operator for a period can be efficiently represented using a matrix-product operator. We first benchmark the method by comparing to exact diagonalization for small systems. We then obtain Floquet eigenstates for larger systems and show unambiguously that the characteristic area-law scaling remains robust.