Anderson localization and many-body localization -- nonequilibrium perspective

A cartoon phase diagram of the spinless fermion model in 1D with long-range hopping at strong disorder without (bottom panel) and with (top panel) long-range interaction. Adapted from Phys. Rev. B 95, 094205 (2017)

Crystalline solids are made of a sea of electrons in a highly ordered microscopic structure of a lattice of positive ions that extends in all directions. In an ordered crystal, the electronic wave function within some energy bands is spread (delocalized) over the periodic potential of the lattice. Now consider adding impurities to the system. The potential is not periodic anymore. The electronic wave function tends to localize around the impurity. Beyond a certain amount of impurity the spread of electronic wave function over real space ceases altogether resulting in an insulating state, or in other words, the wave function becomes localized. This phenomenon is known as Anderson localization (AL) after its discoverer P. W. Anderson.

AL is due to wave interference between multiple scattering paths and is well understood for particles/waves (e.g. electrons, photons, phonons) that do not interact in a disordered medium. Further investigations of localization in disordered media in the presence of short-range interactions between quantum particles led to the concept of many-body localization (MBL). MBL is also an insulator and results from the interplay of disorder and interaction between particles. The nature of MBL in more than one spatial dimension is yet not entirely understood.

We have studied dynamics especially nonequilibrium dynamics in disordered models of electrons, phonons and spins displaying AL and/or MBL. For example, we have calculated system-size scaling of heat current through random lattice models connected to heat baths at the boundaries. Recently, we investigated entanglement dynamics in one-dimensional long-range models of spinless fermions and made an analogy to infer features of AL and MBL in higher-dimensional short-range models. Our these studies are applying the LEGF method, invariant embedding technique, and simulation using classical molecular dynamics and exact diagonalizations.

D Roy and N Kumar, Phys. Rev. B 76, 092202 (2007)

D. Roy and A. Dhar, Phys. Rev. E 78, 051112 (2008)

A. Chaudhuri, A. Kundu, D. Roy, A. Dhar, J. L. Lebowitz, and H. Spohn, Phys. Rev. B 81, 064301 (2010)

D. Roy, R. Singh, and R. Moessner, Phys. Rev. B 92, 180205 (R) (2015)

R. Singh, R. Moessner, and D. Roy, Phys. Rev. B 95, 094205 (2017)