### Abstract

We study anisotropic quantum spin chains in an aperiodic magnetic field h_{n} = λ cos(2φσn^{v}); for 0 < v < 1. For v equal to unity and σ equal to the golden mean, the system is quasiperiodic. In the isotropic limit, the incommensurate behaviour is described by the Harper equation exhibiting the metal-insulator transition whereas in the anisotropic case a new fat critical phase is observed between the extended and localized phases. For v different from unity, the global extended phase of the quasiperiodic anisotropic model is replaced by the metal-insulator transition with mobility edges. The mobility edge corresponding to the isotropic model exhibits a novel intermittency. In addition, a new mobility edge with no analog in the isotropic model appears at energy corresponding to the spin space anisotropy g. Instead of the fat critical phase of the quasiperiodic model we now observe a phase which is localized everywhere except at the energy equal to g. There is no localization-delocalization transition in this case. Various high precision numerical tools suggest the existence of critical states at the onset of metal-insulator transition, along the line where the energy is equal to g as well as at the conformally invariant point. We conjecture that the existence of critical states at a conformal point is a universal phenomenon for all aperiodic potentials.

Original language | English |
---|---|

Pages (from-to) | 614-623 |

Number of pages | 10 |

Journal | Physica Scripta |

Volume | 52 |

Issue number | 6 |

DOIs | |

Publication status | Published - 1 Dec 1995 |

MoE publication type | Not Eligible |

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*Physica Scripta*,

*52*(6), 614-623. https://doi.org/10.1088/0031-8949/52/6/002

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*Physica Scripta*, vol. 52, no. 6, pp. 614-623. https://doi.org/10.1088/0031-8949/52/6/002

**Quantum spin chains in aperiodic magnetic fields.** / Chaves, Juan C.; Satija, Indubala I.; Ketoja, Jukka A.

Research output: Contribution to journal › Article › Scientific › peer-review

TY - JOUR

T1 - Quantum spin chains in aperiodic magnetic fields

AU - Chaves, Juan C.

AU - Satija, Indubala I.

AU - Ketoja, Jukka A.

PY - 1995/12/1

Y1 - 1995/12/1

N2 - We study anisotropic quantum spin chains in an aperiodic magnetic field hn = λ cos(2φσnv); for 0 < v < 1. For v equal to unity and σ equal to the golden mean, the system is quasiperiodic. In the isotropic limit, the incommensurate behaviour is described by the Harper equation exhibiting the metal-insulator transition whereas in the anisotropic case a new fat critical phase is observed between the extended and localized phases. For v different from unity, the global extended phase of the quasiperiodic anisotropic model is replaced by the metal-insulator transition with mobility edges. The mobility edge corresponding to the isotropic model exhibits a novel intermittency. In addition, a new mobility edge with no analog in the isotropic model appears at energy corresponding to the spin space anisotropy g. Instead of the fat critical phase of the quasiperiodic model we now observe a phase which is localized everywhere except at the energy equal to g. There is no localization-delocalization transition in this case. Various high precision numerical tools suggest the existence of critical states at the onset of metal-insulator transition, along the line where the energy is equal to g as well as at the conformally invariant point. We conjecture that the existence of critical states at a conformal point is a universal phenomenon for all aperiodic potentials.

AB - We study anisotropic quantum spin chains in an aperiodic magnetic field hn = λ cos(2φσnv); for 0 < v < 1. For v equal to unity and σ equal to the golden mean, the system is quasiperiodic. In the isotropic limit, the incommensurate behaviour is described by the Harper equation exhibiting the metal-insulator transition whereas in the anisotropic case a new fat critical phase is observed between the extended and localized phases. For v different from unity, the global extended phase of the quasiperiodic anisotropic model is replaced by the metal-insulator transition with mobility edges. The mobility edge corresponding to the isotropic model exhibits a novel intermittency. In addition, a new mobility edge with no analog in the isotropic model appears at energy corresponding to the spin space anisotropy g. Instead of the fat critical phase of the quasiperiodic model we now observe a phase which is localized everywhere except at the energy equal to g. There is no localization-delocalization transition in this case. Various high precision numerical tools suggest the existence of critical states at the onset of metal-insulator transition, along the line where the energy is equal to g as well as at the conformally invariant point. We conjecture that the existence of critical states at a conformal point is a universal phenomenon for all aperiodic potentials.

UR - http://www.scopus.com/inward/record.url?scp=84970080548&partnerID=8YFLogxK

U2 - 10.1088/0031-8949/52/6/002

DO - 10.1088/0031-8949/52/6/002

M3 - Article

AN - SCOPUS:84970080548

VL - 52

SP - 614

EP - 623

JO - Physica Scripta

JF - Physica Scripta

SN - 0031-8949

IS - 6

ER -