Spectral Functions of an Extended Antiferromagnetic $S=1/2$ Heisenberg Model on the Triangular Lattice

TL;DR

This study investigates the spectral properties of an extended antiferromagnetic spin-1/2 Heisenberg model on a triangular lattice, revealing distinct signatures of various quantum phases including spin liquids and magnetic orders through advanced tensor network simulations.

Contribution

It provides high-resolution dynamical responses of the model's phases using GPU-optimized matrix product state simulations, identifying spectral signatures of ordered and liquid regimes.

Findings

Identification of gapless Goldstone modes in ordered phases

Evidence of a U(1) Dirac spin liquid in the spin-liquid regime

Detection of spinon continua and collective modes in chiral spin liquids

Abstract

We study an extended spin-$1/2$ antiferromagnetic Heisenberg model on the triangular lattice, which includes both nearest- and next-nearest-neighbor interactions, as well as a scalar chiral term. This model exhibits a rich phase diagram featuring several competing phases: different quantum spin liquids and various magnetically ordered states, including coplanar $120^\circ$ order, stripe order, and non-coplanar tetrahedral order. We employ large-scale matrix product state simulations optimized for GPUs to obtain high-resolution dynamical responses. Our calculations reveal the spectral features across both ordered and liquid regimes of the phase diagram, which we analyze in comparison with analytical predictions and field-theoretical approaches. We identify unique signatures of the ordered phases in the form of gapless Goldstone modes at the ordering wave vectors. Our results in the $J_1-J_2$ quantum spin-liquid regime are indicative of a $U(1)$ Dirac spin liquid. In the chiral spin-liquid phase, we find signatures of spinons as the fractional excitations of the underlying theory, manifested as the onset of a two-spinon continuum that agrees with predictions from the Kalmeyer-Laughlin ansatz for the ground-state wave function, and collective modes that can be viewed as spinon bound states. We discuss finite-size effects, their consistency with the presumptions from field-theory, and review the dynamical structure factor with regard to experimentally relevant features such as the occurrence of highly dispersive signals and the global distribution of spectral weight.