Phases and phase transitions of an chain on metallic and semimetallic surfaces
Phys. Rev. B 113, 075144 – Published 20 February, 2026
DOI: https://doi.org/10.1103/cvnx-yzwb
Abstract
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 on metallic and semimetallic surfaces. In the strong Kondo coupling 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 the underscreening of the chain, is stable against small values of and is characterized by topological edge modes. The nature of the -driven transitions out of this state depends on the metallic environment. Coupling to a metal (semimetal) constitutes a relevant (irrelevant) perturbation at the decoupled fixed point between the spin-1 chain and the two-dimensional electron gas. In the large positive limit, the system maps onto an anisotropic spin- Kondo system that has been studied. For large negative , in the Ising phase, the spins are frozen. For small values of , the nature of the metallic phase plays a dominant role. On a two-dimensional semimetal, the Kondo coupling is irrelevant at the decoupled fixed point, , leading to a Kondo breakdown phase at weak coupling, irrespective of . In contrast, on a two-dimensional metal, the resulting dissipative Ohmic bath acts as a marginally relevant perturbation at the decoupled fixed point, inducing antiferromagnetic ordering along the spin chain. In this case, drives a spin-flop transition between Ising- and XY-ordered phases. At , we observe continuous transitions between the Kondo breakdown or dissipation-induced long-range ordered phases and the underscreened Haldane phase. This understanding of the phase diagrams is supported by scaling arguments as well as by unbiased, sign-free auxiliary-field quantum Monte Carlo simulations.
