Lieb–Robinson Bounds, Arveson Spectrum and Haag–Ruelle Scattering Theory for Gapped Quantum Spin Systems

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• 作者：Sven Bachmann ; Wojciech Dybalski ; Pieter Naaijkens
• 刊名：Annales Henri Poincare
• 出版年：2016
• 出版时间：July 2016
• 年：2016
• 卷：17
• 期：7
• 页码：1737-1791
• 全文大小：2,051 KB
• 刊物类别：Physics and Astronomy
• 刊物主题：Physics
  Mathematical and Computational Physics
  Dynamical Systems and Ergodic Theory
  Quantum Physics
  Mathematical Methods in Physics
  Relativity and Cosmology
  Elementary Particles and Quantum Field Theory
  
• 出版者：Birkh盲user Basel
• ISSN：1424-0661
• 卷排序：17

文摘

We consider translation invariant gapped quantum spin systems satisfying the Lieb–Robinson bound and containing single-particle states in a ground state representation. Following the Haag–Ruelle approach from relativistic quantum field theory, we construct states describing collisions of several particles, and define the corresponding S-matrix. We also obtain some general restrictions on the shape of the energy–momentum spectrum. For the purpose of our analysis, we adapt the concepts of almost local observables and energy–momentum transfer (or Arveson spectrum) from relativistic QFT to the lattice setting. The Lieb–Robinson bound, which is the crucial substitute of strict locality from relativistic QFT, underlies all our constructions. Our results hold, in particular, in the Ising model in strong transverse magnetic fields.Communicated by Claude Alain Pillet.