Level spectroscopy in a two-dimensional quantum magnet: Linearly dispersing spinons at the deconfined quantum critical point

TL;DR

This paper investigates the excitation spectrum at a deconfined quantum critical point in a 2D quantum magnet, providing evidence for linearly dispersing spinons and symmetry dualities using quantum Monte Carlo simulations.

Contribution

It offers the first quantitative evidence of deconfined spinons with linear dispersion at the critical point in a 2D quantum spin system.

Findings

Deconfined linearly dispersing spinons with gapless points at specific momenta.

Strong evidence for two-spinon excitations in different spin sectors.

Observation of duality between singlet and triplet excitations, suggesting enhanced symmetry.

Abstract

We study the level structure of excitations at the "deconfined" critical point separating antiferromagnetic and valence-bond-solid phases in two-dimensional quantum spin systems using the $J$-$Q$ model as an example. Energy gaps in different spin ($S$) and momentum (${\bf k}$) sectors are extracted from imaginary-time correlation functions obtained in quantum Monte Carlo simulations. We find strong quantitative evidence for deconfined linearly dispersing spinons with gapless points at ${\bf k}=(0,0)$, $(\pi,0)$, $(0,\pi)$, and $(\pi,\pi)$, as inferred from two-spinon excitations ($S=0$ and $S=1$ states) around these points. We also observe a duality between singlet and triplet excitations at the critical point and inside the ordered phases, in support of an enhanced symmetry, possibly SO(5).