The early-time Lieb-Robinson correlation function for qubit arrays

TL;DR

This paper analytically calculates the early-time behavior of the Lieb-Robinson correlation function in qubit arrays, revealing how quantum correlations propagate and how velocity and exponential correlation growth emerge in large systems.

Contribution

It provides the first analytical expression for the leading order of the early-time Lieb-Robinson correlation function in interacting qubit systems.

Findings

Analytical expression for early-time correlation function

Emergence of Lieb-Robinson velocity in large arrays

Exponential growth of correlations at the leading edge

Abstract

The Lieb-Robinson correlation function captures propagation of quantum correlations in a many-body system. We calculate the value of the leading order of the correlation function, not its bound, for a system of interacting qubits at early times. The general analytical result is compared to numerical calculations and is applied to regular qubit lattices in one, two, and three dimensions. The Lieb-Robinson velocity and the approximately exponential leading edge of correlations emerge in the limit of large arrays.