Anomalous symmetries of quantum spin chains and a generalization of the Lieb-Schultz-Mattis theorem

2024/01/04 by Kapustin, Anton, Sopenko, Nikita · 9 citations
#FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Strongly Correlated Electrons (cond-mat.str-el)

paper · doi:10.48550/arxiv.2401.02533

Abstract

For any locality-preserving action of a group G on a quantum spin chain one can define an anomaly index taking values in the group cohomology of G. The anomaly index is a kinematic quantity, it does not depend on the Hamiltonian. We prove that a nonzero anomaly index prohibits any G-invariant Hamiltonian from having G-invariant gapped ground states. Lieb-Schultz-Mattis-type theorems are a special case of this result when G involves translations. In the case when the symmetry group G is a Lie group, we define an anomaly index which takes values in the differentiable group cohomology as defined by J.-L. Brylinski and prove a similar result.

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