@article{ISI:000404978900007,
 abstract = {We review the physics of many-body localization in models with
incommensurate potentials. In particular, we consider one-dimensional
quasiperiodic models with single-particle mobility edges. A conventional
perspective suggests that delocalized states act as a thermalizing bath
for the localized states in the presence of of interactions. However,
contrary to this intuition there is evidence that such systems can
display non-ergodicity. This is in part due to the fact that the
delocalized states do not have any kind of protection due to symmetry or
topology and are thus susceptible to localization. A study of such
incommensurate models, in the non-interacting limit, shows that they
admit extended, partially extended, and fully localized many-body
states. Non-interacting incommensurate models cannot thermalize
dynamically and remain localized upon the introduction of interactions.
In particular, for a certain range of energy, the system can host a
non-ergodic extended (i.e. metallic) phase in which the energy
eigenstates violate the eigenstate thermalization hypothesis (ETH) but
the entanglement entropy obeys volume-law scaling. The level statistics
and entanglement growth also indicate the lack of ergodicity in these
models. The phenomenon of localization and non-ergodicity in a system
with interactions despite the presence of single-particle delocalized
states is closely related to the so-called many-body proximity effect
and can also be observed in models with disorder coupled to systems with
delocalized degrees of freedom. Many-body localization in systems with
incommensurate potentials (without single-particle mobility edges) have
been realized experimentally, and we show how this can be modified to
study the the effects of such mobility edges. Demonstrating the failure
of thermalization in the presence of a single-particle mobility edge in
the thermodynamic limit would indicate a more robust violation of the
ETH.},
 article-number = {1600399},
 author = {Deng, Dong-Ling and Ganeshan, Sriram and Li, Xiaopeng and Modak, Ranjan
and Mukerjee, Subroto and Pixley, J. H.},
 doi = {10.1002/andp.201600399},
 eissn = {1521-3889},
 issn = {0003-3804},
 journal = {ANNALEN DER PHYSIK},
 month = {JUL},
 number = {7},
 researcherid-numbers = {Modak, Ranjan/AAS-4353-2020},
 times-cited = {12},
 title = {Many-body localization in incommensurate models with a mobility edge},
 unique-id = {ISI:000404978900007},
 volume = {529},
 year = {2017}
}