Propagation of quantum fluctuations in quantum Ising model

TL;DR

This paper studies how quantum fluctuations spread in the quantum Ising model, revealing that they propagate faster than excitations in the system's equilibrium state, with implications for understanding entanglement dynamics.

Contribution

It introduces a detailed analysis of quantum fluctuation propagation in the quantum Ising model using large coordination number expansion and compares adiabatic and quench regimes.

Findings

Quantum fluctuations propagate with twice the group speed of excitations.

Propagation speed varies between adiabatic and quench regimes.

Long-range correlations are generated during the quench process.

Abstract

We investigate the entanglement dynamics between two distant qubits by analyzing correlations in the quantum Ising model. Starting from the spin system in a paramagnetic regime enforced by the external magnetic field $B$, we then switch on the ferromagnetic spin-spin coupling $J$. Using the large coordination number expansion, we consider two limiting switching regimes: (1) adiabatic, which monitors the evolution of the ground state through the quantum transition to an ordered state; and (2) instantaneous (quench) which monitors instead the propagation of quantum fluctuations and simulates the generation of long range correlations. In particular, we find that quantum fluctuations propagate with twice the group speed of excitations in the equilibrium state of the system.