Obtaining highly-excited eigenstates of many-body localized Hamiltonians by the density matrix renormalization group

TL;DR

This paper adapts the density-matrix renormalization group method to efficiently find highly excited eigenstates in many-body localized systems, enabling larger system size studies than traditional methods.

Contribution

It introduces a novel adaptation of DMRG tailored for highly excited states in MBL Hamiltonians, leveraging their low entanglement and spatial structure.

Findings

Successfully finds highly excited eigenstates with high accuracy at large disorder

Enables study of larger MBL systems than exact diagonalization allows

Demonstrates the method's effectiveness on the random field Heisenberg model

Abstract

The eigenstates of many-body localized (MBL) Hamiltonians exhibit low entanglement. We adapt the highly successful density-matrix renormalization group method, which is usually used to find modestly entangled ground states of local Hamiltonians, to find individual highly excited eigenstates of many body localized Hamiltonians. The adaptation builds on the distinctive spatial structure of such eigenstates. We benchmark our method against the well studied random field Heisenberg model in one dimension. At moderate to large disorder, we find that the method successfully obtains excited eigenstates with high accuracy, thereby enabling a study of MBL systems at much larger system sizes than those accessible to exact-diagonalization methods.