Dynamical signatures of symmetry-broken and liquid phases in an <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>S</mml:mi></mml:math> = <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mfrac><mml:mn>1</mml:mn><mml:mn>2</mml:mn></mml:mfrac></mml:math> Heisenberg antiferromagnet on the triangular lattice
Markus Drescher, Laurens Vanderstraeten, Roderich Moessner, Frank Pollmann
Abstract
We present the dynamical spin structure factor of the antiferromagnetic spin-$\frac{1}{2} {J}_{1}\text{\ensuremath{-}}{J}_{2}$ Heisenberg model on a triangular lattice obtained from large-scale matrix-product state simulations. The high frustration due to the combination of antiferromagnetic nearest- and next-nearest-neighbor interactions yields a rich phase diagram. We resolve the low-energy excitations both in the ${120}^{\ensuremath{\circ}}$ ordered phase and in the putative spin-liquid phase at ${J}_{2}/{J}_{1}=0.125$. In the ordered phase, we observe an avoided decay of the lowest magnon branch, demonstrating the robustness of this phenomenon in the presence of gapless excitations. Our findings in the spin-liquid phase chime with the field-theoretical predictions for a gapless Dirac spin liquid, in particular the picture of low-lying monopole excitations at the corners of the Brillouin zone. We comment on possible practical difficulties of distinguishing proximate liquid and solid phases based on the dynamical structure factor.