Ground states of the XY-model

Huzihiro Araki, Taku Matsui

Research output: Contribution to journalArticle

33 Citations (Scopus)

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 languageEnglish
Pages (from-to)213-245
Number of pages33
JournalCommunications in Mathematical Physics
Volume101
Issue number2
DOIs
Publication statusPublished - Jun 1 1985
Externally publishedYes

Fingerprint

XY Model
Ground State
ground state
Nonuniqueness
uniqueness
Irreducible Representation
Ising
Solitons
broken symmetry
Sector
sectors
Uniqueness
solitary waves
Symmetry

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

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

In: Communications in Mathematical Physics, Vol. 101, No. 2, 01.06.1985, p. 213-245.

Research output: Contribution to journalArticle

Araki, Huzihiro ; Matsui, Taku. / Ground states of the XY-model. In: Communications in Mathematical Physics. 1985 ; Vol. 101, No. 2. pp. 213-245.
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