Dynamical dimer structure factor of the triangular $S=1/2$ Heisenberg antiferromagnet

TL;DR

This paper uses large-scale GPU-accelerated matrix-product-state simulations to analyze the dynamical dimer structure factor in the triangular $S=1/2$ Heisenberg antiferromagnet, revealing insights into various ordered and quantum spin-liquid phases.

Contribution

It provides the first detailed dynamical dimer response analysis across multiple phases, supporting the existence of a $U(1)$ Dirac quantum spin liquid with gapless singlet monopole excitations.

Findings

Low-energy modes below the two-magnon continuum in ordered phases.

Observation of dispersion minima at half the Brillouin zone corners in the gapless QSL.

Support for a $U(1)$ Dirac QSL with gapless singlet monopole excitations.

Abstract

The dynamical dimer structure factor is an observable probing spin-singlet excitations of quantum magnets distinct from those commonly studied by the spin structure factor. We report the dimer response for the extended spin-$1/2$ antiferromagnetic Heisenberg model on the triangular lattice using large-scale GPU-accelerated matrix-product-state simulations. We investigate the ordered phases with $120^\circ$ coplanar, collinear stripe, and tetrahedral spin order, as well as candidate quantum spin-liquid (QSL) regimes, comprising an expected gapless $U(1)$ Dirac QSL and a chiral QSL at finite spin-scalar-chirality coupling. In the ordered phases, we find low-energy modes below the onset of the two-magnon continuum illustrating avoided quasiparticle decay. Within the candidate gapless QSL, we observe absolute dispersion minima at momenta of half the Brillouin zone corners, $X\equiv K/2$, in agreement with field-theory predictions that singlet monopole excitations of the $U(1)$ Dirac spin liquid become gapless at these points. Thus, the high-resolution dynamical dimer response provides support for a $U(1)$ Dirac QSL with singlet monopole excitations.