Local critical behaviour at aperiodic surface extended perturbation in the Ising quantum chain

TL;DR

This paper investigates the critical behavior at the surface of a quantum Ising chain with aperiodic surface perturbations, revealing how marginal modulations affect surface exponents and order at criticality.

Contribution

It provides exact calculations of surface magnetic exponents and conjectures the surface energy density exponent in an aperiodically modulated quantum Ising model.

Findings

Surface order exists at the bulk critical point above a critical modulation amplitude.

Surface magnetic exponents are exactly calculated.

Surface energy density exponent is conjectured from finite-size scaling.

Abstract

The surface critical behaviour of the semi--infinite one--dimensional quantum Ising model in a transverse field is studied in the presence of an aperiodic surface extended modulation. The perturbed couplings are distributed according to a generalized Fredholm sequence, leading to a marginal perturbation and varying surface exponents. The surface magnetic exponents are calculated exactly whereas the expression of the surface energy density exponent is conjectured from a finite--size scaling study. The system displays surface order at the bulk critical point, above a critical value of the modulation amplitude. It may be considered as a discrete realization of the Hilhorst--van Leeuwen model.