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Main Authors: He, Cheng-Hao, You, Yi-Zhuang, Xu, Xiao Yan
Format: Preprint
Published: 2026
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Online Access:https://arxiv.org/abs/2603.18285
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author He, Cheng-Hao
You, Yi-Zhuang
Xu, Xiao Yan
author_facet He, Cheng-Hao
You, Yi-Zhuang
Xu, Xiao Yan
contents Symmetry plays a central role in modern physics, from classifying quantum states to characterizing phases of matter through spontaneous symmetry breaking. In interacting fermionic systems with multiple internal degrees of freedom, however, determining the full continuous symmetry group and classifying possible order parameters remain challenging. In this work, we present a systematic framework for analyzing continuous symmetries and identifying candidate order parameters in such systems. By mapping the Hamiltonian to a Majorana representation, we obtain the generators of continuous symmetries from the Lie algebra of operators that commute with the Hamiltonian. We then identify the structure of this Lie algebra using the theory of semisimple Lie algebras. Building on representation theory, we further develop a systematic method for exhaustively enumerating candidate order parameters. By decomposing the exterior-power representations induced by the symmetry algebra on the Majorana space and incorporating discrete lattice symmetries, we classify these order parameters according to the symmetries they break. (Abridged. Please see the PDF manuscript for the complete abstract and specific model applications.)
format Preprint
id arxiv_https___arxiv_org_abs_2603_18285
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Continuous symmetry analysis and systematic identification of candidate order parameters for interacting fermion models
He, Cheng-Hao
You, Yi-Zhuang
Xu, Xiao Yan
Strongly Correlated Electrons
High Energy Physics - Theory
Quantum Physics
Symmetry plays a central role in modern physics, from classifying quantum states to characterizing phases of matter through spontaneous symmetry breaking. In interacting fermionic systems with multiple internal degrees of freedom, however, determining the full continuous symmetry group and classifying possible order parameters remain challenging. In this work, we present a systematic framework for analyzing continuous symmetries and identifying candidate order parameters in such systems. By mapping the Hamiltonian to a Majorana representation, we obtain the generators of continuous symmetries from the Lie algebra of operators that commute with the Hamiltonian. We then identify the structure of this Lie algebra using the theory of semisimple Lie algebras. Building on representation theory, we further develop a systematic method for exhaustively enumerating candidate order parameters. By decomposing the exterior-power representations induced by the symmetry algebra on the Majorana space and incorporating discrete lattice symmetries, we classify these order parameters according to the symmetries they break. (Abridged. Please see the PDF manuscript for the complete abstract and specific model applications.)
title Continuous symmetry analysis and systematic identification of candidate order parameters for interacting fermion models
topic Strongly Correlated Electrons
High Energy Physics - Theory
Quantum Physics
url https://arxiv.org/abs/2603.18285