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## Abstract

We compute critical properties of a general class of quantum spin chains which are quadratic in the Fermi operators and can be solved exactly under certain symmetry constraints related to the classical compact groups U(N),O(N), and Sp(2N). In particular we calculate critical exponents s,ν, and z, corresponding to the energy gap, correlation length, and dynamic exponent, respectively. We also compute the ground state correlators ⟨σxiσxi+n⟩g,⟨σyiσyi+n⟩g, and ⟨∏ni=1σzi⟩g, all of which display quasi-long-range order with a critical exponent dependent upon system parameters. Our approach establishes universality of the exponents for the class of systems in question.

Original language | English |
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Article number | 032106 |

Number of pages | 6 |

Journal | Physical Review E: Statistical, Nonlinear, and Soft Matter Physics |

Volume | 92 |

Issue number | 3 |

DOIs | |

Publication status | Published - 4 Sept 2015 |

### Bibliographical note

Date of Acceptance: 18/08/2015## Fingerprint

Dive into the research topics of 'Random matrix theory and critical phenomena in quantum spin chains'. Together they form a unique fingerprint.## Projects

- 2 Finished