One of the most timely topics in condensed matter theory is many-body localization, where researchers try to understand the intricate interplay of disorder and interactions. The many-body localized phase has many intriguing properties: it is a perfect finite temperature insulator, fails to thermalize and is robust against changes in the microscopic Hamiltonian. Moreover, interactions can lead to delocalization, stabilizing an ergodic phase and thus a novel transition from that ergodic phase into the many-body localized (MBL) phase.
In our recent work, we introduce the analysis of one-particle density matrices as a new framework to understand many-body localization from a single-particle perspective. Our key results are that eigenstates of one-particle density matrices behave very analogous to the eigenstates of the Anderson problem: they are localized in the MBL and extended in the ergodic phase. Most importantly, the MBL phase is quite similar to a Fermi liquid: both states emerge adiabatically out of noninteracting reference states (the Anderson insulator versus the noninteracting Fermi gas) and possess quasi-particles. In the MBL phase, these quasi-particles are localized in real space, with the eigenstates of one-particle density matrices providing the optimized single-particle approximation. Moreover, the occupation spectrum, i.e., the eigenvalues of one-particle density matrices, feature a discontinuity, just like in a Fermi liquid, where the discontinuity is proportional to the quasi-particle weight. This discontinuity, finite in the MBL phase but zero in the ergodic phase, provides a useful means to compute phase diagrams, as the figure shows. For more details, see: Bera, Schomerus, Heidrich-Meisner, Bardarson, Phys. Rev. Lett. 115, 046603 (2015)