Phases and phase transitions of an S = 3 2 chain on metallic and semimetallic surfaces

Motivated by recent scanning tunneling microscopy experiments on chains of Co adatoms on Cu surfaces, we investigate the physics of a spin-3/2 Heisenberg chain with single-ion anisotropy (D) on metallic and semi-metallic surfaces. In the strong Kondo coupling (Jₖ) limit, a perturbative analysis maps the system onto a Haldane spin-1 chain with single-ion anisotropy, ferromagnetically coupled to the metallic surface. This Haldane state, arising from underscreening of the S=3/2 chain, is stable against small D and characterized by topological edge modes. The nature of the D-driven transitions out of this state depends on the environment. Coupling to a metal (semi-metal) is a relevant (irrelevant) perturbation at the decoupled fixed point between the spin-1 chain and the two-dimensional electron gas. In the large positive D limit, the system maps onto an anisotropic spin-1/2 Kondo system. For large negative D, in the Ising phase, spins are frozen. For small Jₖ, the nature of the metallic phase dominates. On a two-dimensional semi-metal, the Kondo coupling is irrelevant at the decoupled fixed point (Jₖ= 0), leading to a Kondo breakdown phase at weak coupling, irrespective of D. In contrast, on a two-dimensional metal, the resulting dissipative Ohmic bath is a marginally relevant perturbation, inducing antiferromagnetic ordering along the chain. In this case, D drives a spin-flop transition between Ising and XY ordered phases. At D=0, we observe continuous transitions between the Kondo breakdown or dissipation-induced long-range ordered phases and the underscreened Haldane phase. These phase diagrams are supported by scaling arguments and sign-free auxiliary-field quantum Monte Carlo simulations.