Gappability Index for Quantum Many-Body Systems.
Phys Rev Lett
; 129(1): 017204, 2022 Jul 01.
Article
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| ID: mdl-35841555
ABSTRACT
We propose an index I_{G} which characterizes the degree of gappability, namely the difficulty to induce a unique ground state with a nonvanishing excitation gap, in the presence of a symmetry G. I_{G} represents the dimension of the subspace of ambient uniquely gapped theories in the entire G-invariant "theory space." The celebrated Lieb-Schultz-Mattis theorem corresponds, in our formulation, to the case I_{G}=0 (completely ingappable) for the symmetry G including the lattice translation symmetry. We illustrate the usefulness of the index by discussing the phase diagram of spin-1/2 antiferromagnets in various dimensions, which do not necessarily have the translation symmetry.
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Phys Rev Lett
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2022
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