TY - JOUR
T1 - On the regime of localized excitations for disordered oscillator systems
AU - Abdul-Rahman, Houssam
AU - Sims, Robert
AU - Stolz, Günter
N1 - Funding Information:
G. S. gratefully acknowledges hospitality and support at the Centre de Recherches Mathématiques of the Université de Montréal, where part of this work was done during the Thematic Semester on Mathematical challenges in many-body physics and quantum information.
Publisher Copyright:
© 2020, Springer Nature B.V.
PY - 2020/6/1
Y1 - 2020/6/1
N2 - We study quantum oscillator lattice systems with disorder, in arbitrary dimension, requiring only partial localization of the associated effective one-particle Hamiltonian. This leads to a many-body localized regime of excited states with arbitrarily large energy density. We prove zero-velocity Lieb–Robinson bounds for the dynamics of Weyl operators as well as for position and momentum operators restricted to this regime. Dynamical localization is also shown in the form of quasi-locality of the time evolution of local Weyl operators and through exponential clustering of the dynamic correlations of states with localized excitations.
AB - We study quantum oscillator lattice systems with disorder, in arbitrary dimension, requiring only partial localization of the associated effective one-particle Hamiltonian. This leads to a many-body localized regime of excited states with arbitrarily large energy density. We prove zero-velocity Lieb–Robinson bounds for the dynamics of Weyl operators as well as for position and momentum operators restricted to this regime. Dynamical localization is also shown in the form of quasi-locality of the time evolution of local Weyl operators and through exponential clustering of the dynamic correlations of states with localized excitations.
KW - Exponential clustering
KW - Lieb–Robinson bounds
KW - Localization
KW - Quantum oscillator systems
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U2 - 10.1007/s11005-020-01256-2
DO - 10.1007/s11005-020-01256-2
M3 - Article
AN - SCOPUS:85078437126
SN - 0377-9017
VL - 110
SP - 1159
EP - 1189
JO - Letters in Mathematical Physics
JF - Letters in Mathematical Physics
IS - 6
ER -