Boundary conditions and amplitude ratios for finite-size corrections of a one-dimensional quantum spin model

TL;DR

This paper investigates how boundary conditions affect finite-size corrections in a 1D quantum spin model, deriving universal amplitude ratios that align with conformal field theory predictions.

Contribution

It introduces two new sets of universal amplitude ratios for finite-size corrections under different boundary conditions, validated by perturbative conformal field theory.

Findings

Derived universal amplitude ratios for free and antiperiodic boundary conditions.

Confirmed agreement with conformal field theory predictions.

Provided exact and perturbative calculations for finite-size effects.

Abstract

We study the influence of boundary conditions on the finite-size corrections of a one-dimensional (1D) quantum spin model by exact and perturbative theoretic calculations. We obtain two new infinite sets of universal amplitude ratios for the finite-size correction terms of the 1D quantum spin model of $N$ sites with free and antiperiodic boundary conditions. The results for the lowest two orders are in perfect agreement with a perturbative conformal field theory scenario proposed by Cardy [Nucl. Phys. B {\bf 270}, 186 (1986)].