Obtaining Highly Excited Eigenstates of Many-Body Localized Hamiltonians by the Density Matrix Renormalization Group Approach

Vedika Khemani, Frank Pollmann, and S. L. Sondhi

Phys. Rev. Lett. 116, 247204 – Published 17 June 2016

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 MBL 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, 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.

Received 8 November 2015

DOI:https://doi.org/10.1103/PhysRevLett.116.247204

Physics Subject Headings (PhySH)

Many-body localization

Density matrix renormalization group

Condensed Matter, Materials & Applied PhysicsStatistical Physics & Thermodynamics

Authors & Affiliations

Vedika Khemani^1,2, Frank Pollmann², and S. L. Sondhi^1,2

¹Physics Department, Princeton University, Princeton, New Jersey 08544, USA
²Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Strasse 38, 01187 Dresden, Germany