General Lieb-Schultz-Mattis type theorems for quantum spin chains

Abstract

We develop a general operator algebraic method which focuses on projective representations of symmetry group for proving Lieb-Schultz-Mattis type theorems, i.e., no-go theorems that rule out the existence of a unique gapped ground state (or, more generally, a pure split state), for quantum spin chains with on-site symmetry. We first prove a theorem for translation invariant spin chains that unifies and extends two theorems proved by two of the authors in [OT1]. We then prove a Lieb-Schultz-Mattis type theorem for spin chains that are invariant under the reflection about the origin and not necessarily translation invariant.

arXiv comment22 pages; v2: typos corrected and references added; the reference [OT1] in the abstract refers to arXiv:1808.08740

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