Quantum Phase Transitions of Frustrated Heisenberg Antiferromagnets: a Comprehensive Renormalization Approach

TL;DR

This paper introduces a comprehensive renormalization method for frustrated quantum antiferromagnets, accurately capturing spin-wave interactions across the entire Brillouin zone and elucidating phase transitions in the $J_1$-$J_2$ model.

Contribution

It presents a novel renormalization approach that treats all spin-wave modes uniformly, providing new insights into phase transitions and low-energy magnon properties in frustrated antiferromagnets.

Findings

Unified description of second-order and first-order phase transitions.

Explicit calculations of spin stiffness and spin-wave velocity.

Accurate treatment of high-energy and low-energy spin-wave modes.

Abstract

We develop a novel renormalization approach for frustrated quantum antiferromagnets. It is designed to consistently treat spin-wave interactions all over the magnetic Brillouin zone, including high-energy modes in outer regions as well as low energy modes in the center. Focusing on the paradigmatic $J_1$-$J_2$ model, we find a unifying description of the second-order transition between the N\'eel phase and the paramagnetic phase and the first-order transition between the N\'eel phase and the columnar phase. Our approach provides explicit results for the renormalized values of the spin stiffness and spin-wave velocity characterizing the low-energy magnons in the N\'eel phase.