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arXiv · 2406.06414

Quadratic dispersion relations in gapless frustration-free systems

Rintaro Masaoka·Tomohiro Soejima·Haruki Watanabe
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Abstract

Recent case-by-case studies revealed that the dispersion of low energy excitations in gapless frustration-free Hamiltonians is often quadratic or softer. In this work, we argue that this is actually a general property of such systems. By combining a previous study by Bravyi and Gosset and the min-max principle, we prove this hypothesis for models with local Hilbert spaces of dimension two that contains only nearest-neighbor interactions on cubic lattice. This may be understood as a no-go theorem realizing gapless phases with linearly dispersive excitations in frustration-free Hamiltonians. We also provide examples of frustration-free Hamiltonians in which the plane-wave state of a single spin flip does not constitute low energy excitations.

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Rintaro Masaoka, Tomohiro Soejima, Haruki Watanabe. 2024-06-10. Quadratic dispersion relations in gapless frustration-free systems. https://doi.org/10.1103/physrevb.110.195140

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