Nature of quantum spin liquids of the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>S</mml:mi><mml:mo>=</mml:mo><mml:mfrac><mml:mn>1</mml:mn><mml:mn>2</mml:mn></mml:mfrac></mml:mrow></mml:math> Heisenberg antiferromagnet on the triangular lattice: A parallel DMRG study
Yi‐Fan Jiang, Hong‐Chen Jiang
Abstract
We study the ground-state properties of the quantum spin liquid (QSL) phases of the spin-$1/2$ antiferromagnetic Heisenberg model on the triangular lattice with nearest- $({J}_{1})$, next-nearest- $({J}_{2})$, and third-neighbor $({J}_{3})$ interactions by using the density-matrix renormalization group (DMRG) method. By combining parallel DMRG with $\mathrm{SU}(2)$ spin rotational symmetry, we are able to obtain accurate results on large cylinders with length up to ${L}_{x}=48$ and circumference ${L}_{y}=6--12$. Our results suggest that the QSL phase of the ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ Heisenberg model is gapped, which is characterized by the absence of a gapless mode and by short-range spin-spin and dimer-dimer correlations. In the presence of ${J}_{3}$ interaction, we find that a critical QSL with a single gapless mode emerges. While both spin-spin and scalar chiral-chiral correlations are short ranged, dimer-dimer correlations are quasi long ranged and decay as a power law at long distances.