Deconfined quantum criticality in a spin chain with long-range interactions

We study a 1D spin-1/2 model with long-range power-law decaying unfrustrated (bipartite) Heisenberg exchange interactions J_r ∝ r^-α (for odd distances r) and a competing multi-spin interaction Q favoring a dimerized (valence-bond solid, VBS) ground state. Employing quantum Monte Carlo techniques and Lanczos exact diagonalization, we analyze order parameters and excited-state level crossings to characterize quantum phase transitions between the different ground states hosted by the model in the (α, Q) plane. For 1 < α < 1.3, we find a direct continuous quantum phase transition between a long-range ordered antiferromagnetic state and a VBS state, providing an analogy to the two-dimensional deconfined quantum-critical point. Unlike previous 1D analogies of deconfined quantum criticality, where the two ordered phases both have fractional excitations, in our model the excitations fractionalize at the critical point, changing from anomalous, sublinealy dispersing spin waves in the antiferromagnetic phase to deconfined spinons in the VBS phase. We extract critical exponents and also use order-parameter histograms to study possible emergent symmetries.