Kink correlations, domain size distribution, and the emptiness formation probability after the Kibble-Zurek quench in the quantum Ising chain

TL;DR

This paper investigates the correlations and domain size distributions in the quantum Ising chain after a Kibble-Zurek quench, revealing how dephasing affects kink correlations and the quantum state structure.

Contribution

It introduces a detailed analysis of quadratic correlators and their dependence on dephasing length, providing new insights into the post-quench quantum state and related measurable quantities.

Findings

Dephasing length exceeds KZ length logarithmically.

Anomalous correlators are suppressed by slower ramps.

Pfaffian formulas enable analytic asymptotes for domain size distributions.

Abstract

Linear quench of the transverse field drives the quantum Ising chain across a quantum critical point from the paramagnetic to the ferromagnetic phase. We focus on normal and anomalous quadratic correlators between fermionic kink creation and annihilation operators. They depend not only on the Kibble-Zurek (KZ) correlation length but also on a dephasing length scale, which differs from the KZ length by a logarithmic correction. Additional slowing down of the ramp in the ferromagnetic phase further increases the dephasing length and suppresses the anomalous correlator. The quadratic correlators enter Pfaffians that yield experimentally relevant kink correlation functions, the probability distribution of ferromagnetic domain sizes, and, closely related, emptiness formation probability. The latter takes the form of a Pfaffian of a block Toeplitz matrix that allows for some analytic asymptotes. Finally, we obtain further insight into the structure of the state at the end of the ramp by interpreting it as a paired state of fermionic kinks characterized by its pair wave function. All those quantities are sensitive to quantum coherence between eigenstates with different numbers of kinks, thus making them a convenient probe of the quantumness of a quantum simulator platform.