Origin of nonsymmorphic bosonization formulas in generalized antiferromagnetic Kitaev spin-$\frac{1}{2}$ chains from a renormalization-group perspective

TL;DR

This paper uses renormalization group analysis to explain the origin of nonsymmorphic symmetry effects in bosonization formulas of generalized antiferromagnetic Kitaev spin chains, revealing how U(1) symmetry breaking arises.

Contribution

It provides a RG-based explanation for the nonsymmorphic bosonization formulas and the origin of U(1) symmetry breaking in the Kitaev spin-1/2 chains.

Findings

U(1) symmetry breaking originates from wavefunction renormalization effects.

RG analysis predicts signs and magnitudes of bosonization coefficients.

Nonsymmorphic symmetry effects are rooted in microscopic U(1) breaking interactions.

Abstract

Recently, in the Luttinger liquid phase of the one-dimensional generalized antiferromagnetic Kitaev spin-1/2 model, it has been found that the abelian bosonization formulas of the local spin operators only respect the exact discrete nonsymmorphic symmetry group of the model, not the emergent U(1) symmetry. In this work, we perform a renormalization group (RG) study to provide explanations for the origin of the U(1) breaking terms in the bosonization formulas. We find that the lack of U(1) symmetry originates from the wavefunction renormalization effects in the spin operators along the RG flow induced by the U(1) breaking interactions in the microscopic Hamiltonian. In addition, the RG analysis can give predictions to the signs and order of magnitudes of the coefficients in the bosonization formulas. Our work is helpful to understand the rich nonsymmorphic physics in one-dimensional Kitaev spin models.