2016/10/31 by Houssam Abdul‐Rahman, Houssam Abdul-Rahman, Bruno Nachtergaele +2
Mathematics · Physics and Astronomy · #Chain (unit) #Classical XY model #Condensed matter physics #Materials science #Model Reduction and Neural Networks #Opinion Dynamics and Social Influence #Phase transition #Physics #Quantum many-body systems #Quantum mechanics #Spin (aerodynamics) #Thermodynamics #math-ph #math.MP #msc:82B44 #quant-ph
paper · pdf · doi:10.1002/andp.201600280
published as Ann. Phy. (Berlin) 529, No. 7, 1600280 (2017) · Final version, to appear in Annalen der Physik; title modified, introduction expanded, references added, new Lemma 8.1
arxiv created 2017/02/26 · openalex publication_date 2017/03/24 · arxiv updated 2018/02/23 · openalex created_date 2022/10/03 · openalex updated_date 2026/08/05
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.