Lieb-Schultz-Mattis theorem with a local twist for general one-dimensional quantum systems

Hal Tasaki

doi:10.1007/s10955-017-1946-0

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arXiv · 1708.05186

Lieb-Schultz-Mattis theorem with a local twist for general one-dimensional quantum systems

Hal Tasaki

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Abstract

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 wth 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.

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Hal Tasaki. 2017-08-17. Lieb-Schultz-Mattis theorem with a local twist for general one-dimensional quantum systems. https://doi.org/10.1007/s10955-017-1946-0

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