Critical properties of the one-dimensional spin-1/2 antiferromagnetic Heisenberg model in the presence of a uniform field

TL;DR

This paper investigates the critical behavior of the 1D spin-1/2 antiferromagnetic Heisenberg model under a uniform magnetic field, analyzing excitation energies, structure factors, and comparing with conformal field theory predictions.

Contribution

It provides a detailed analysis of critical quantities and their finite-size scaling, offering new insights into the model's behavior in a magnetic field.

Findings

Identification of soft mode momenta and zero frequency excitations

Analysis of singularities in structure factors

Comparison with conformal field theory predictions

Abstract

In the presence of a uniform field the one-dimensional spin-$\frac{1}{2}$ antiferromagnetic Heisenberg model develops zero frequency excitations at field-dependent 'soft mode' momenta. We determine three types of critical quantities, which we extract from the finite-size dependence of the lowest excitation energies, the singularities in the static structure factors and the infrared singularities in the dynamical structure factors at the soft mode momenta. We also compare our results with the predictions of conformal field theory.