976 research outputs found
Localization of interacting fermions at high temperature
We suggest that if a localized phase at nonzero temperature exists for
strongly disordered and weakly interacting electrons, as recently argued, it
will also occur when both disorder and interactions are strong and is very
high. We show that in this high- regime the localization transition may be
studied numerically through exact diagonalization of small systems. We obtain
spectra for one-dimensional lattice models of interacting spinless fermions in
a random potential. As expected, the spectral statistics of finite-size samples
cross over from those of orthogonal random matrices in the diffusive regime at
weak random potential to Poisson statistics in the localized regime at strong
randomness. However, these data show deviations from simple one-parameter
finite-size scaling: the apparent mobility edge ``drifts'' as the system's size
is increased. Based on spectral statistics alone, we have thus been unable to
make a strong numerical case for the presence of a many-body localized phase at
nonzero
Phenomenology of fully many-body-localized systems
We consider fully many-body localized systems, i.e. isolated quantum systems
where all the many-body eigenstates of the Hamiltonian are localized. We define
a sense in which such systems are integrable, with localized conserved
operators. These localized operators are interacting pseudospins, and the
Hamiltonian is such that unitary time evolution produces dephasing but not
"flips" of these pseudospins. As a result, an initial quantum state of a
pseudospin can in principle be recovered via (pseudospin) echo procedures. We
discuss how the exponentially decaying interactions between pseudospins lead to
logarithmic-in-time spreading of entanglement starting from nonentangled
initial states. These systems exhibit multiple different length scales that can
be defined from exponential functions of distance; we suggest that some of
these decay lengths diverge at the phase transition out of the fully many-body
localized phase while others remain finite.Comment: 5 pages. Some of this paper has already appeared in: Huse and
Oganesyan, arXiv:1305.491
Many-Body Localization in a Quasiperiodic System
Recent theoretical and numerical evidence suggests that localization can
survive in disordered many-body systems with very high energy density, provided
that interactions are sufficiently weak. Stronger interactions can destroy
localization, leading to a so-called many-body localization transition. This
dynamical phase transition is relevant to questions of thermalization in
extended quantum systems far from the zero-temperature limit. It separates a
many-body localized phase, in which localization prevents transport and
thermalization, from a conducting ("ergodic") phase in which the usual
assumptions of quantum statistical mechanics hold. Here, we present numerical
evidence that many-body localization also occurs in models without disorder but
rather a quasiperiodic potential. In one dimension, these systems already have
a single-particle localization transition, and we show that this transition
becomes a many-body localization transition upon the introduction of
interactions. We also comment on possible relevance of our results to
experimental studies of many-body dynamics of cold atoms and non-linear light
in quasiperiodic potentials.Comment: (12 pages + 3 page appendix, 11 figures) This version has been
accepted to PRB. We have clarified certain points and slightly modified the
organization of the paper in response to comments by two referee
- …