Schwinger-boson approach to quantum spin systems: Gaussian fluctuactions in the "natural" gauge

TL;DR

This paper refines the Schwinger-boson approach by calculating Gaussian fluctuations, revealing a quantum nonmagnetic phase in the J1-J2 antiferromagnet, with results aligning well with numerical data.

Contribution

It introduces a method to include Gaussian fluctuations in the Schwinger-boson framework, improving predictions of quantum phases in frustrated spin systems.

Findings

Identification of a quantum nonmagnetic phase between J2/J1 ratios of 0.53 and 0.64

Good agreement with numerical results on finite clusters

Avoidance of infrared divergencies in the thermodynamic limit

Abstract

We compute the Gaussian-fluctuation corrections to the saddle-point Schwinger-boson results using collective coordinate methods. Concrete application to investigate the frustrated J1-J2 antiferromagnet on the square lattice shows that, unlike the saddle-point predictions, there is a quantum nonmagnetic phase for 0.53 < J2/J1 < 0.64. This result is obtained by considering the corrections to the spin stiffness on large lattices and extrapolating to the thermodynamic limit, which avoids the infinite-lattice infrared divergencies associated to Bose condensation. The very good agreement of our results with exact numerical values on finite clusters lends support to the calculational scheme employed.