## Abstract

The ground-states of the spin-S antiferromagnetic chain H_{AF} with a projection-based interaction and the spin-1/2 XXZ-chain H_{XXZ} at anisotropy parameter Δ = cosh (λ) share a common loop representation in terms of a two-dimensional functional integral which is similar to the classical planar Q-state Potts model at Q=2S+1=2cosh(λ). The multifaceted relation is used here to directly relate the distinct forms of translation symmetry breaking which are manifested in the ground-states of these two models: dimerization for H_{AF} at all S> 1 / 2 , and Néel order for H_{XXZ} at λ> 0. The results presented include: (i) a translation to the above quantum spin systems of the results which were recently proven by Duminil–Copin–Li–Manolescu for a broad class of two-dimensional random-cluster models, and (ii) a short proof of the symmetry breaking in a manner similar to the recent structural proof by Ray–Spinka of the discontinuity of the phase transition for Q> 4. Altogether, the quantum manifestation of the change between Q= 4 and Q> 4 is a transition from a gapless ground-state to a pair of gapped and extensively distinct ground-states.

Original language | English (US) |
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Pages (from-to) | 2737-2774 |

Number of pages | 38 |

Journal | Annales Henri Poincare |

Volume | 21 |

Issue number | 8 |

DOIs | |

State | Published - Aug 1 2020 |

## All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Nuclear and High Energy Physics
- Mathematical Physics