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arXiv · 2004.06458

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

Yoshiko Ogata·Yuji Tachikawa·Hal Tasaki
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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.

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Yoshiko Ogata, Yuji Tachikawa, Hal Tasaki. 2020-04-14. General Lieb-Schultz-Mattis type theorems for quantum spin chains. https://doi.org/10.1007/s00220-021-04116-9

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