Ground state degeneracy in quantum spin systems protected by crystal symmetries

2017/05/25 by Yang Qi, Chen Fang, Qi, Yang +3 · 1 citation
Chemistry · Physics and Astronomy · #Advanced NMR Techniques and Applications #FOS: Physical sciences #Molecular spectroscopy and chirality #Quantum many-body systems #Strongly Correlated Electrons (cond-mat.str-el)

paper · pdf · doi:10.48550/arxiv.1705.09190

openalex publication_date 2017/05/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We develop a no-go theorem for two-dimensional bosonic systems with crystal symmetries: if there is a half-integer spin at a rotation center, where the point-group symmetry is \mathbb D_2,4,6, such a system must have a ground-state degeneracy protected by the crystal symmetry. Such a degeneracy indicates either a broken-symmetry state or a unconventional state of matter. Comparing to the Lieb-Schultz-Mattis Theorem, our result counts the spin at each rotation center, instead of the total spin per unit cell, and therefore also applies to certain systems with an even number of half-integer spins per unit cell.

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