### Abstract

We study the dynamics of the entanglement spectrum, that is the time evolution of the eigenvalues of the reduced density matrices after a bipartition of a one-dimensional spin chain. Starting from the ground state of an initial Hamiltonian, the state of the system is evolved in time with a new Hamiltonian. We consider both instantaneous and quasi adiabatic quenches of the system Hamiltonian across a quantum phase transition. We analyse the Ising model that can be exactly solved and the XXZ for which we employ the time-dependent density matrix renormalisation group algorithm. Our results show once more a connection between the Schmidt gap, i.e. the difference of the two largest eigenvalues of the reduced density matrix and order parameters, in this case the spontaneous magnetisation.

Original language | English |
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Article number | P06001 |

Number of pages | 19 |

Journal | Journal of Statistical Mechanics: Theory and Experiment |

Volume | 2014 |

Issue number | 6 |

DOIs | |

Publication status | Published - 9 Jun 2014 |

### Keywords

- density matrix renormalisation group calculations
- entanglement in extended quantum systems (theory)
- ladders and planes (theory)
- quantum quenches
- spin chains
- entanglement spectrum

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## Cite this

*Journal of Statistical Mechanics: Theory and Experiment*,

*2014*(6), [P06001]. https://doi.org/10.1088/1742-5468/2014/06/P06001