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

The low-energy spectrum of antiferromagnets reveals valuable information about the nature of the phases or phase transitions in such systems. Discussed in this talk are 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 (k) sectors are extracted from imaginary-time correlation functions obtained in quantum Monte Carlo simulations using methods developed in. Strong quantitative evidence is found for deconfined linearly dispersing spinons with gapless points at k = (0,0), (π,0), (0,π) and (π,π), as inferred from singlet (S=0) and triplet (S=1) excitations around these points. It is observed that 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). Discussed here is another lattice model, the easy-plane J-Q model, that hosts both deconfined quantum criticality and a first-order transition between the easy-plane antiferromagnetic and valence-bond-solid states, depending on a single anisotropy parameter