TY - JOUR
T1 - Localization properties of the disordered XY spin chain
T2 - A review of mathematical results with an eye toward many-body localization
AU - Abdul-Rahman, Houssam
AU - Nachtergaele, Bruno
AU - Sims, Robert
AU - Stolz, Günter
N1 - Publisher Copyright:
© 2017 by WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
PY - 2017/7
Y1 - 2017/7
N2 - We review several aspects of Many-Body Localization-like properties exhibited by the disordered XY chains: localization properties of the energy eigenstates and thermal states, propagation bounds of Lieb-Robinson type, decay of correlation functions, absence of particle transport, bounds on the bipartite entanglement, and bounded entanglement growth under the dynamics. We also prove new results on the absence of energy transport and Fock space localization. All these properties are made accessible to mathematical analysis due to the exact mapping of the XY chain to a system of quasi-free fermions given by the Jordan-Wigner transformation. Motivated by these results we discuss conjectured properties of more general disordered quantum spin and other systems as possible directions for future mathematical research.
AB - We review several aspects of Many-Body Localization-like properties exhibited by the disordered XY chains: localization properties of the energy eigenstates and thermal states, propagation bounds of Lieb-Robinson type, decay of correlation functions, absence of particle transport, bounds on the bipartite entanglement, and bounded entanglement growth under the dynamics. We also prove new results on the absence of energy transport and Fock space localization. All these properties are made accessible to mathematical analysis due to the exact mapping of the XY chain to a system of quasi-free fermions given by the Jordan-Wigner transformation. Motivated by these results we discuss conjectured properties of more general disordered quantum spin and other systems as possible directions for future mathematical research.
KW - Anderson Model
KW - Area Law
KW - Dynamical Localization
KW - Entanglement Entropy
KW - Fock Space Localization
KW - Many-Body Localization
KW - XY chain
KW - Zero-Velocity Lieb-Robinson Bounds
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U2 - 10.1002/andp.201600280
DO - 10.1002/andp.201600280
M3 - Review article
AN - SCOPUS:85021782787
SN - 0003-3804
VL - 529
JO - Annalen der Physik
JF - Annalen der Physik
IS - 7
M1 - 1600280
ER -