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Deconfined quantum criticality in spin-1/2 chains with long-range interactions

We study spin-$1/2$ chains with long-range power-law decaying unfrustrated (bipartite) Heisenberg exchange $J_r \propto r^{-α}$ and multi-spin interactions $Q$ favoring a valence-bond solid (VBS) ground state. Employing quantum Monte Carlo techniques and Lanczos diagonalization, we analyze order parameters and excited-state level crossings to characterize quantum states and phase transitions in the $(α,Q)$ plane. For weak $Q$ and sufficiently slowly decaying Heisenberg interactions (small $α$), the system has a long-range-ordered antiferromagnetic (AFM) ground state, and upon increasing $α$ there is a continuous transition into a quasi long-range ordered (QLRO) critical state of the type in the standard Heisenberg chain. For rapidly decaying long-range interactions, there is transition between QLRO and VBS ground states of the same kind as in the frustrated $J_1$-$J_2$ Heisenberg chain. Our most important finding is a direct continuous quantum phase transition between the AFM and VBS states - a close analogy to the 2D deconfined quantum-critical point. In previous 1D analogies the ordered phases both have gapped fractional excitations, and the critical point is a conventional Luttinger Liquid. In our model the excitations fractionalize upon transitioning from the AFM state, changing from spin waves to deconfined spinons. We extract critical exponents at the AFM-VBS transition and use order-parameter distributions to study emergent symmetries. We find emergent O($4$) symmetry of the O($3$) AFM and scalar VBS order parameters. Thus, the order parameter fluctuations exhibit the covariance of a uniaxially deformed O($4$) sphere (an "elliptical" symmetry). This unusual quantum phase transition does not yet have any known field theory description, and our detailed results can serve to guide its construction. We discuss possible experimental realizations.