Extracting Quantum Many-Body Scarred Eigenstates with Matrix Product States

TL;DR

This paper introduces a matrix-product-state algorithm called DMRG-S to efficiently identify and analyze quantum many-body scarred eigenstates in large systems, revealing new scar states and addressing their stability.

Contribution

The paper presents a novel MPS-based algorithm for extracting scarred eigenstates in large systems, enabling systematic identification and analysis without prior knowledge.

Findings

Successfully extracted scarred eigenstates in 80-site chains.

Discovered new scarred eigenstates with exact MPS representations.

Provided insights into the stability of Néel state revivals in the thermodynamic limit.

Abstract

Quantum many-body scarred systems host nonthermal excited eigenstates immersed in a sea of thermal ones. In cases where exact expressions for these special eigenstates are not known, it is computationally demanding to distinguish them from their exponentially many thermal neighbors. We propose a matrix-product-state (MPS) algorithm, dubbed DMRG-S, to extract such states at system sizes far beyond the scope of exact diagonalization. Using this technique, we obtain scarred eigenstates in Rydberg-blockaded chains of up to 80 sites and perform a finite-size scaling study to address the lingering question of the stability for the N\'eel state revivals in the thermodynamic limit. Our method also provides a systematic way to obtain exact MPS representations for scarred eigenstates near the target energy without a priori knowledge. In particular, we find several new scarred eigenstates with exact MPS representations in kinetically constrained spin and clock models. The combination of numerical and analytical investigations in our work provides a new methodology for future studies of quantum many-body scars.