Quadratic dispersion relations in gapless frustration-free systems

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.

9 pages, 2 figure; published version

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• Quasi-local Frustration-Free Free Fermions
• Frustration-free free fermions
• Frustration-free free fermions and beyond
• Exact steady states and fragmentation-induced relaxation in the no-passing asymmetric simple exclusion process