Boundary effects in the critical scaling of entanglement entropy in 1D systems

TL;DR

This paper investigates how open boundaries affect entanglement entropy in critical 1D spin chains, revealing boundary-induced oscillations and their decay, with analytical and numerical insights across different anisotropies.

Contribution

It provides exact numerical and analytical analysis of boundary effects on entanglement entropy in critical XXZ chains, including a new logarithmic correction at the isotropic point.

Findings

Open boundaries induce alternating terms in entropy and energy density.

The decay of boundary effects follows a power-law with anisotropy-dependent exponents.

A logarithmic correction is analytically derived at the isotropic point.

Abstract

We present exact diagonalization and density matrix renormalization group results for the entanglement entropy of critical spin-1/2 XXZ chains. We find that open boundary conditions induce an alternating term in both the energy density and the entanglement entropy which are approximately proportional, decaying away from the boundary with a power-law. The power varies with anisotropy along the XXZ critical line and is corrected by a logarithmic factor, which we calculate analytically, at the isotropic point. A heuristic resonating valence bond explanation is suggested.