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

### 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.

###### Current status:
Editor-in-charge assigned

### Submission & Refereeing History

Submission 1906.00948v1 on 8 June 2019