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This preprint presents a theoretical framework for zero-point theorems within quantum spin systems, establishing model-independent constraints on critical phenomena across various dimensions without relying on specific low-energy dynamics. By extending conventional arguments to multi-parameter Hamiltonian families, the work offers universal insights into relevant operators governing phase diagrams in high-dimensional settings.
Zero-point theorems in quantum many-body physics
arXiv:2608.15542v1 Announce Type: cross Abstract: We propose several zero-point type arguments based on the inevitable zero point(s) of a spectral gap in the quantum spin system phase diagrams in various dimensions. We consider multi-parameter families of Hamiltonian extending the conventional zero-point theorem that includes only one parameter. Analogously to the zero-point theorem, we only impose model-independent transformation relations along the parameter boundary, rather than specifying any low-energy dynamics or response. We further give a series of conjectures, which generalize our statements in a uniform way. Our results give powerful and universal model-independent constraints on the possible relevant operators for critical phenomena in quantum spin models in arbitrary high dimensions.
Abstract:We propose several zero-point type arguments based on the inevitable zero point(s) of a spectral gap in the quantum spin system phase diagrams in various dimensions. We consider multi-parameter families of Hamiltonian extending the conventional zero-point theorem that includes only one parameter. Analogously to the zero-point theorem, we only impose model-independent transformation relations along the parameter boundary, rather than specifying any low-energy dynamics or response. We further give a series of conjectures, which generalize our statements in a uniform way. Our results give powerful and universal model-independent constraints on the possible relevant operators for critical phenomena in quantum spin models in arbitrary high dimensions.
Strongly Correlated Electrons (cond-mat.str-el); Statistical Mechanics (cond-mat.stat-mech); High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph); Quantum Physics (quant-ph)
arXiv:2608.15542 [cond-mat.str-el]
(or arXiv:2608.15542v1 [cond-mat.str-el] for this version)
https://doi.org/10.48550/arXiv.2608.15542 arXiv-issued DOI via DataCite (pending registration)
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