Quantum phases in the honeycomb-lattice <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>J</mml:mi><mml:mn>1</mml:mn></mml:msub></mml:math>–<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>J</mml:mi><mml:mn>3</mml:mn></mml:msub></mml:math> ferro-antiferromagnetic model

Abstract

Using large-scale density-matrix renormalzation group calculations and minimally augmented spin-wave theory, we demonstrate that the phase diagram of the quantum $S=\frac{1}{2}\phantom{\rule{4pt}{0ex}}{J}_{1}$--${J}_{3}$ ferro-antiferromagnetic model on the honeycomb lattice differs dramatically from the classical one. It hosts the double-zigzag and Ising-$z$ phases as unexpected intermediaries between ferromagnetic and zigzag states that are also extended beyond their classical regions of stability. In broad agreement with quantum order-by-disorder arguments, these collinear phases replace the classical spiral state.

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