Translational symmetry breaking and soliton sectors for massive quantum spin models in 1 + 1 dimensions

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Abstract

We consider the classification of pure infinite volume ground states and that of soliton sectors for 1+1 dimensional massive quantum spin models. We obtain a proof that non-translationally invariant ground state cannot exist for a class of translationally invariant Hamiltonians including the spin 1 AKLT (Affleck Kennedy Lieb Tasaki) antiferromagnetic spin model. We also obtain a complete classification of soliton sectors (up to unitary equivalence) for certain massive models (e.g. ferromagnetic XXZ models).

Original languageEnglish
Pages (from-to)127-144
Number of pages18
JournalCommunications in Mathematical Physics
Volume189
Issue number1
DOIs
Publication statusPublished - Jan 1 1997

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All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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