Long-range entanglement from spontaneous non-onsite symmetry breaking

• URL: http://arxiv.org/abs/2411.05004v1
• Date: Thu, 07 Nov 2024 18:59:51 GMT
• Title: Long-range entanglement from spontaneous non-onsite symmetry breaking
• Authors: Zhehao Zhang, Yabo Li, Tsung-Cheng Lu,
• Abstract summary: We show a frustration-free lattice model exhibiting SSB of a non-onsite symmetry. We analytically prove the two-fold ground-state degeneracy and the existence of a finite energy gap. Our work reveals the exotic features of SSB of non-onsite symmetries, which may lie beyond the framework of topological holography.
• Score: 3.3754780158324564
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• Abstract: We explore the states of matter arising from the spontaneous symmetry breaking (SSB) of $\mathbb{Z}_2$ non-onsite symmetries. In one spatial dimension, we construct a frustration-free lattice model exhibiting SSB of a non-onsite symmetry, which features the coexistence of two ground states with distinct symmetry-protected topological (SPT) orders. We analytically prove the two-fold ground-state degeneracy and the existence of a finite energy gap. Fixing the symmetry sector yields a long-range entangled ground state that features long-range correlations among non-invertible charged operators. We also present a constant-depth measurement-feedback protocol to prepare such a state with a constant success probability in the thermodynamic limit, which may be of independent interest. Under a symmetric deformation, the SSB persists up to a critical point, beyond which a gapless phase characterized by a conformal field theory emerges. In two spatial dimensions, the SSB of 1-form non-onsite symmetries leads to a long-range entangled state (SPT soup) - a condensate of 1d SPT along any closed loops. On a torus, there are four such locally indistinguishable states that exhibit algebraic correlations between local operators, which we derived via a mapping to the critical $O(2)$ loop model. This provides an intriguing example of `topological quantum criticality'. Our work reveals the exotic features of SSB of non-onsite symmetries, which may lie beyond the framework of topological holography (SymTFT).

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