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

Understand

We study spin-$1/2$ chains with long-range power-law decaying unfrustrated (bipartite) Heisenberg exchange $J_r \propto r^{-\alpha}$ 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 $(\alpha,Q)$ plane.
• For weak $Q$ and sufficiently slowly decaying Heisenberg interactions (small $\alpha$), the system has a long-range-ordered antiferromagnetic (AFM) ground state, and upon increasing $\alpha$ 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.