The ground state in quantum mechanics is always unique
The claim that the ground state in quantum mechanics is always unique is refuted by multiple theoretical and physical models, such as supersymmetric systems and frustrated lattices, which frequently exhibit ground-state degeneracy.
The claim states that the quantum mechanical ground state is always unique. However, degenerate ground states are a well-known phenomenon in quantum mechanics, occurring in the presence of certain symmetries (e.g., supersymmetric models, conformal field theories, or geometrically frustrated systems like artificial spin ice). Papers [0], [6], and [10] all discuss systems or models with degenerate ground states, directly contradicting the claim.
Asao Arai. On the degeneracy in the ground state of the <i>N</i>=2 Wess–Zumino supersymmetric quantum mechanics. 1989. https://doi.org/10.1063/1.528485
Paper [0] demonstrates the existence of degenerate zero-energy ground states in supersymmetric quantum mechanical models.
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Alissa Furet, Theo Johnson-Freyd. Ground-state degeneracy of twisted sectors of Conway moonshine SCFT. 2025. https://doi.org/10.1090/conm/813/16284
Paper [6] calculates ground state degeneracies in twisted sectors of conformal field theories, noting that multiple states can share the ground state energy.
Lara Braga de Oliveira. Nanofabrication and investigation of ground state degeneracy in artificial spin ice lattices. https://doi.org/10.47328/ufvbbt.2024.733
Paper [10] investigates systems like artificial spin ice lattices designed specifically to exhibit high ground-state degeneracy.
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