Emergent continuous symmetry and ground-state factorization induced by long-range interactions

• URL: http://arxiv.org/abs/2510.08391v2
• Date: Mon, 13 Oct 2025 14:20:32 GMT
• Title: Emergent continuous symmetry and ground-state factorization induced by long-range interactions
• Authors: Yue Yu, Myung-Joong Hwang,
• Abstract summary: We present a theory in which the low-lying excitation in the broken-symmetry phase acquires a continuous symmetry.<n>A striking consequence of the emergent continuous symmetry and conservation law is that it constrains quantum correlations in the ground-state to be zero.<n>Our finding is a universal feature of quantum phase transitions in fully-connected systems and in their lattice generalizations.
• Score: 11.51075495217878
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The spontaneous breaking of a $Z_2$ symmetry typically gives rise to emergent excitations possessing the same symmetry with a renormalized mass. Contrary to this conventional wisdom, we present a theory in which the low-lying excitation in the broken-symmetry phase acquires a continuous symmetry, even when the underlying symmetry of the system is discrete. In the presence of anisotropic long-range interactions, the order parameter renormalizes the relative strength of the particle-conserving and particle-nonconserving interactions. When one of the two renormalized interactions vanishes, a conservation law absent in the original Hamiltonian emerges, giving rise to a continuous symmetry. A striking consequence of the emergent continuous symmetry and conservation law is that it constrains quantum correlations in the ground-state to be zero, leading to the ground-state factorization in the presence of strong interactions. Our finding is a universal feature of quantum phase transitions in fully-connected systems and in their lattice generalizations; therefore, it can be observed in a wide range of physical systems.

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