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

Mario Collura

SciPost Phys. 7, 072 (2019) · published 2 December 2019

- doi: 10.21468/SciPostPhys.7.6.072
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### 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 a 3-states classical 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 show 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.

### Ontology / Topics

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^{1 }^{2 }^{3 }Mario Collura

^{1}Scuola Internazionale Superiore di Studi Avanzati / International School for Advanced Studies [SISSA]^{2}Università degli Studi di Padova / University of Padua [UNIPD]^{3}Universität des Saarlandes / Saarland University

- European Commission [EC]
- Horizon 2020 (through Organization: European Commission [EC])