Rotational invariance and order-parameter stiffness in frustrated quantum spin systems

TL;DR

This paper uses the Schwinger-boson method to analyze how quantum fluctuations affect the order-parameter stiffness in frustrated spin systems, revealing stability of magnetic order in some cases and disorder in others.

Contribution

It provides a detailed calculation of Gaussian-fluctuation corrections to the stiffness in frustrated quantum spin models, highlighting methodological improvements in the Schwinger-boson approach.

Findings

Stiffness weakens but order persists in the triangular-lattice antiferromagnet.

Stiffness vanishes in the J1-J2 model within a specific frustration window.

Finite cluster analysis with twisted boundary conditions improves Schwinger-boson predictions.

Abstract

We compute, within the Schwinger-boson scheme, the Gaussian-fluctuation corrections to the order-parameter stiffness of two frustrated quantum spin systems: the triangular-lattice Heisenberg antiferromagnet and the J1-J2 model on the square lattice. For the triangular-lattice Heisenberg antiferromagnet we found that the corrections weaken the stiffness, but the ground state of the system remains ordered in the classical 120 spiral pattern. In the case of the J1-J2 model, with increasing frustration the stiffness is reduced until it vanishes, leaving a small window 0.53 < J2/J1 < 0.64 where the system has no long-range magnetic order. In addition, we discuss several methodological questions related to the Schwinger-boson approach. In particular, we show that the consideration of finite clusters which require twisted boundary conditions to fit the infinite-lattice magnetic order avoids the use of ad hoc factors to correct the Schwinger-boson predictions.