## SciPost Submission Page

# Relaxation of the order-parameter statistics in the Ising quantum chain

### by Mario Collura

### Submission summary

As Contributors: | Mario Collura |

Arxiv Link: | https://arxiv.org/abs/1906.00948v1 |

Date submitted: | 2019-06-08 |

Submitted by: | Collura, Mario |

Submitted to: | SciPost Physics |

Domain(s): | Theoretical |

Subject area: | Quantum Physics |

### Abstract

We study the out-of-equilibrium probability distribution function of the local order parameter in the transverse field Ising quantum chain. Starting from a fully polarised state, the relaxation of the ferromagnetic order is analysed: we obtain a full analytical description of the late-time stationary distribution by means of a remarkable relation to the partition function of the 3-states Potts model. Accordingly, depending on the phase whereto the post-quench Hamiltonian belongs, the probability distribution may locally retain memories of the initial long-range order. When quenching deep in the broken-symmetry phase, we proof that the stationary order-parameter statistics is indeed related to that of the ground state. We highlight this connection by inspecting the ground-state equilibrium properties, where we propose an effective description based on the block-diagonal approximation of the $n$-point spin correlation functions.