Density Profiles in Random Quantum Spin Chains

TL;DR

This paper investigates magnetization and energy-density profiles in large random quantum spin chains, demonstrating that their scaling functions align with theoretical predictions from conformal invariance and Fisher-de Gennes conjecture.

Contribution

It provides numerical evidence that magnetization profiles in random transverse-field Ising chains follow conformal invariance and Fisher-de Gennes scaling, supported by analytic expressions.

Findings

Magnetization profiles collapse to universal scaling functions.

Scaling functions match predictions from conformal invariance.

Numerical data supports Fisher-de Gennes scaling conjecture.

Abstract

We consider random transverse-field Ising spin chains and study the magnetization and the energy-density profiles by numerically exact calculations in rather large finite systems ($L\le 128$). Using different boundary conditions (free, fixed and mixed) the numerical data collapse to scaling functions, which are very accurately described by simple analytic expressions. The average magnetization profiles satisfy the Fisher-de Gennes scaling conjecture and the corresponding scaling functions are indistinguishable from those predicted by conformal invariance.