Dynamics of the order-parameter statistics in the long-range Ising model

TL;DR

This paper investigates how the probability distribution of the order parameter in a long-range quantum Ising model evolves over time after a quench, revealing different dynamical regimes influenced by interaction range and topological defects.

Contribution

It introduces a detailed analysis of the order-parameter distribution dynamics in a long-range Ising model, highlighting the impact of interaction decay exponent on relaxation and gaussification.

Findings

Different dynamical regimes identified based on interaction range.

Gaussification can be slowed or broken by confinement effects.

Behavior depends critically on the decay exponent of interactions.

Abstract

We study the relaxation of the local ferromagnetic order in the transverse field quantum Ising chain with power-law decaying interactions $1/r^{\alpha}$. We prepare the system in the GHZ state and study the time evolution of the probability distribution function (PDF) of the order-parameter within a block of $l$ when quenching the transverse field. The model is known to support long-range order at finite temperature for $\alpha \leq 2.0$ . In this regime, quasi-localized topological magnetic defects are expected to strongly affect the equilibration of the full probability distribution. We highlight different dynamical regimes where gaussification mechanism may be slowed down by confinement and eventually breaks. We further study the PDF dynamics induced by changing the effective dimensionality of the system; we mimic this by quenching the range of the interactions. As a matter of fact, the behavior of the system crucially depends on the value of $\alpha$ governing the unitary evolution.