### Abstract

The zero-temperature XX chain is studied with emphasis on the properties of a block of L spins inside the chain. We investigate the quantum fluctuations resulting from the entanglement of the block with the rest of the chain using analytical as well as numerical (density matrix renormalization group) methods. It is found that the rest of the chain acts as a thermal environment and an effective temperature can be introduced to describe the fluctuations. We show that the effective temperature description is robust in the sense that several independent definitions (through the fluctuation dissipation theorem, comparing with a finite temperature system) yield the same functional form in the limit of large block size (L → ∞). The effective temperature can also be shown to satisfy the basic requirements on how it changes when two bodies of equal or unequal temperatures are brought into contact.

Original language | English |
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Article number | P11013 |

Journal | Journal of Statistical Mechanics: Theory and Experiment |

Issue number | 11 |

DOIs | |

Publication status | Published - Nov 1 2006 |

### Keywords

- Density matrix renormalization group calculations
- Entanglement in extended quantum systems (theory)
- Ladders and planes (theory)
- Spin chains

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Statistics and Probability
- Statistics, Probability and Uncertainty