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

Understand

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.