title: Obtaining Highly Excited Eigenstates of Many-Body Localized Hamiltonians by the Density Matrix Renormalization Group Approach.
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.
authors.affiliation: Physics Department, Princeton University, Princeton, New Jersey 08544, USA.|Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Strasse 38, 01187 Dresden, Germany.
authors.forename: Vedika
authors.initials: V
authors.lastname: Khemani
authors.affiliation: Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Strasse 38, 01187 Dresden, Germany.
authors.forename: Frank
authors.initials: F
authors.lastname: Pollmann
authors.affiliation: Physics Department, Princeton University, Princeton, New Jersey 08544, USA.|Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Strasse 38, 01187 Dresden, Germany.
authors.forename: S L
authors.initials: SL
authors.lastname: Sondhi