### Abstract

Ground states of the X Y-model on infinite one-dimensional lattice, specified by the Hamiltonian {Mathematical expression} with real parameters J≠0, γ and λ, are all determined. The model has a unique ground state for |λ|≧1, as well as for γ=0, |λ|<1; it has two pure ground states (with a broken symmetry relative to the 180° rotation of all spins around the z-axis) for |λ|<1, γ≠0, except for the known Ising case of λ=0, |λ|=1, for which there are two additional irreducible representations (soliton sectors) with infinitely many vectors giving rise to ground states. The ergodic property of ground states under the time evolution is proved for the uniqueness region of parameters, while it is shown to fail (even if the pure ground states are considered) in the case of non-uniqueness region of parameters.

Original language | English |
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Pages (from-to) | 213-245 |

Number of pages | 33 |

Journal | Communications in Mathematical Physics |

Volume | 101 |

Issue number | 2 |

DOIs | |

Publication status | Published - Jun 1 1985 |

Externally published | Yes |

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### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

*Communications in Mathematical Physics*,

*101*(2), 213-245. https://doi.org/10.1007/BF01218760

**Ground states of the XY-model.** / Araki, Huzihiro; Matsui, Taku.

Research output: Contribution to journal › Article

*Communications in Mathematical Physics*, vol. 101, no. 2, pp. 213-245. https://doi.org/10.1007/BF01218760

}

TY - JOUR

T1 - Ground states of the XY-model

AU - Araki, Huzihiro

AU - Matsui, Taku

PY - 1985/6/1

Y1 - 1985/6/1

N2 - Ground states of the X Y-model on infinite one-dimensional lattice, specified by the Hamiltonian {Mathematical expression} with real parameters J≠0, γ and λ, are all determined. The model has a unique ground state for |λ|≧1, as well as for γ=0, |λ|<1; it has two pure ground states (with a broken symmetry relative to the 180° rotation of all spins around the z-axis) for |λ|<1, γ≠0, except for the known Ising case of λ=0, |λ|=1, for which there are two additional irreducible representations (soliton sectors) with infinitely many vectors giving rise to ground states. The ergodic property of ground states under the time evolution is proved for the uniqueness region of parameters, while it is shown to fail (even if the pure ground states are considered) in the case of non-uniqueness region of parameters.

AB - Ground states of the X Y-model on infinite one-dimensional lattice, specified by the Hamiltonian {Mathematical expression} with real parameters J≠0, γ and λ, are all determined. The model has a unique ground state for |λ|≧1, as well as for γ=0, |λ|<1; it has two pure ground states (with a broken symmetry relative to the 180° rotation of all spins around the z-axis) for |λ|<1, γ≠0, except for the known Ising case of λ=0, |λ|=1, for which there are two additional irreducible representations (soliton sectors) with infinitely many vectors giving rise to ground states. The ergodic property of ground states under the time evolution is proved for the uniqueness region of parameters, while it is shown to fail (even if the pure ground states are considered) in the case of non-uniqueness region of parameters.

UR - http://www.scopus.com/inward/record.url?scp=0038717760&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0038717760&partnerID=8YFLogxK

U2 - 10.1007/BF01218760

DO - 10.1007/BF01218760

M3 - Article

AN - SCOPUS:0038717760

VL - 101

SP - 213

EP - 245

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

IS - 2

ER -