Entanglement in spin chains with gradients

TL;DR

This paper investigates how entanglement entropy behaves in spin chains with linearly varying fields or couplings, revealing different growth patterns after quenches in XX and Ising models.

Contribution

It provides an exact analysis of entanglement in inhomogeneous spin chains and characterizes the dynamics after quenches, including different growth laws for various models.

Findings

Entanglement entropy scales logarithmically with interface width.

Post-quench entropy growth is logarithmic in time for XX model.

Post-quench entropy growth is quadratic in time for transverse Ising chain.

Abstract

We study solvable spin chains where either fields or couplings vary linearly in space and create a sandwich-like structure of the ground state. We find that the entanglement entropy between two halves of a chain varies logarithmically with the interface width. After quenching to a homogeneous critical system, the entropy grows logarithmically in time in the XX model, but quadratically in the transverse Ising chain. We explain this behaviour and indicate generalizations to other power laws.