Gradient critical phenomena in the Ising quantum chain: surface behaviour

TL;DR

This paper develops a scaling theory for the surface behavior of the Ising quantum chain under power-law deviations from criticality, supported by exact and numerical results.

Contribution

It introduces a new length scale to describe surface critical phenomena with power-law perturbations, validated by exact and numerical analysis.

Findings

Scaling theory accurately predicts surface behavior

Exact results for linear perturbations confirm the theory

Numerical studies support the theory for quadratic perturbations

Abstract

We consider the influence of a power-law deviation from the critical coupling such that the system is critical at its surface. We develop a scaling theory showing that such a perturbation introduces a new length scale which governs the scaling behaviour of the density profiles as well as the finite-size behaviour of the surface properties. Exact results are obtained for the Ising quantum chain when the perturbation varies linearly whereas the quadratic perturbation is mainly studied numerically. The scaling theory is well confirmed in both cases.