Cluster Condensation and Symmetry-Protected Thermal Rigidity of Bose gases on the Haldane Sphere

Meng-Jie Wang; Jun-Hui Zheng

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arXiv · 2611.02799

Cluster Condensation and Symmetry-Protected Thermal Rigidity of Bose gases on the Haldane Sphere

Meng-Jie Wang·Jun-Hui Zheng

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Abstract

We show that a spinless Bose gas on a Haldane sphere with a small monopole charge $q$ realizes, in the lowest Landau level (LLL), an exactly solvable SU(2)-protected cluster condensate: a Hafnian condensate of two-boson singlets for $q=1$, analogous to resonating-valence-bond singlet coverings, and a four-boson singlet condensate for $q=3/2$. Unlike topologically protected quantum Hall states, the exactness of these states relies only on SU(2) symmetry and repulsiveness, with no pseudopotential fine-tuning. Their SU(2)-protected degeneracy renders the single-particle correlations exactly temperature-independent even as the clusters dissociate, a thermal rigidity absent in conventional Bose--Einstein condensates (BECs). Increasing the interaction drives a transition to a vortex BEC with spontaneously broken rotational symmetry.

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Meng-Jie Wang, Jun-Hui Zheng. 2026-11-02. Cluster Condensation and Symmetry-Protected Thermal Rigidity of Bose gases on the Haldane Sphere. https://arxiv.org/abs/2611.02799

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