C 1-Classification of Gapped Parent Hamiltonians of Quantum Spin Chains

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• 作者：Sven Bachmann ; Yoshiko Ogata
• 刊名：Communications in Mathematical Physics
• 出版年：2015
• 出版时间：September 2015
• 年：2015
• 卷：338
• 期：3
• 页码：1011-1042
• 全文大小：650 KB
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• 作者单位：Sven Bachmann (1)
  Yoshiko Ogata (2)
  
  1. Mathematisches Institut der Universit?t München, Theresienstrasse 39, 80333, Munich, Germany
  2. Graduate School of Mathematical Sciences, The University of Tokyo, Komaba, Tokyo, 153-8914, Japan
  
• 刊物类别：Physics and Astronomy
• 刊物主题：Physics
  Mathematical and Computational Physics
  Quantum Physics
  Quantum Computing, Information and Physics
  Complexity
  Statistical Physics
  Relativity and Cosmology
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1432-0916

文摘

We consider the C 1-classification of gapped Hamiltonians introduced in Fannes et?al. (Commun Math Phys 144:443-90, 1992) and Nachtergaele (Commun Math Phys 175:565-06, 1996) as parent Hamiltonians of translation invariant finitely correlated states. Within this family, we show that the number of edge modes, which is equal at the left and right edge, is the complete invariant. The construction proves that translation invariance of the ‘bulk-ground state does not need to be broken to establish C 1-equivalence, namely that the spin chain does not need to be blocked.