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arXiv · 2112.06575

Gappability Index for Quantum Many-Body Systems

Yuan Yao·Masaki Oshikawa·Akira Furusaki
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Abstract

We propose an index $\mathcal{I}_G$ which characterizes the degree of ingappability, namely the difficulty to induce a unique ground state with a nonvanishing excitation gap, in the presence of a symmetry $G$. $\mathcal{I}_G$ represents the dimension of the subspace of ambient uniquely-gapped in the entire $G$-invariant "theory space". The celebrated Lieb-Schultz-Mattis theorem corresponds, in our formulation, to the case $\mathcal{I}_G=0$ (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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Yuan Yao, Masaki Oshikawa, Akira Furusaki. 2021-12-13. Gappability Index for Quantum Many-Body Systems. https://doi.org/10.1103/physrevlett.129.017204

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