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Lieb–Schultz–Mattis Theorem with a Local Twist for General One-Dimensional Quantum Systems

Journal Article · · Journal of Statistical Physics
 [1]
  1. Gakushuin University, Department of Physics (Japan)

We formulate and prove the local twist version of the Yamanaka–Oshikawa–Affleck theorem, an extension of the Lieb–Schultz–Mattis theorem, for one-dimensional systems of quantum particles or spins. We can treat almost any translationally invariant system with global U(1) symmetry. Time-reversal or inversion symmetry is not assumed. It is proved that, when the “filling factor” is not an integer, a ground state without any long-range order must be accompanied by low-lying excitations whose number grows indefinitely as the system size is increased. The result is closely related to the absence of topological order in one-dimension. The present paper is written in a self-contained manner, and does not require any knowledge of the Lieb–Schultz–Mattis and related theorems.

OSTI ID:
22784010
Journal Information:
Journal of Statistical Physics, Journal Name: Journal of Statistical Physics Journal Issue: 4 Vol. 170; ISSN JSTPBS; ISSN 0022-4715
Country of Publication:
United States
Language:
English