Chain Phase Transitions with Single-Ion Anisotropy Demonstrate Topological Edge Modes in Metallic Environments

The behaviour of atomic chains on metallic surfaces presents a fascinating challenge in condensed matter physics, and recent experiments using scanning tunnelling microscopy have revealed intriguing properties of cobalt atom chains on copper surfaces. Bimla Danu and Fakher F. Assaad, both from Universität Würzburg, investigate the fundamental physics governing these chains, specifically focusing on how interactions with the underlying surface influence their magnetic properties. Their work demonstrates that the surface environment dramatically alters the chain’s behaviour, driving transitions between distinct magnetic states, ranging from frozen spins to long-range order. Crucially, they reveal that metallic surfaces promote antiferromagnetic ordering, while semi-metallic surfaces lead to a breakdown of the interactions between the chain and the surface, establishing a clear link between surface conductivity and magnetic behaviour in these nanoscale systems.

Researchers discovered that strong Kondo coupling transforms the system into a Haldane spin-1 state, which couples to the metallic surface. This Haldane state, stabilized by incomplete screening of magnetic moments, exhibits topological edge modes and remains stable even with small changes in the system. The surrounding environment critically influences the system’s behaviour; coupling to a metal creates a significant effect, while a semi-metal has a negligible one at the system’s fundamental state.

Correlated Electrons, Quantum Magnetism, Numerical Methods

This research program involves developing and refining numerical methods to simulate complex quantum systems, aiming to discover and characterize new states of matter, particularly topological phases, and to understand the interplay between magnetism and superconductivity. Applying these computational methods to real materials is a central goal, as is investigating the connections between condensed matter physics and quantum information processing. Researchers also explore topological phases of matter, including quantum Hall effects and quantum spin liquids, and investigate high-temperature superconductivity. The inclusion of tensor networks and quantum error correction suggests an exploration of connections between strongly correlated systems and quantum information science.

Kondo Coupling Stabilizes Topological Edge Modes

This work presents a detailed investigation into a spin-Heisenberg chain with single-ion anisotropy deposited on metallic and semi-metallic surfaces, motivated by recent scanning tunneling microscopy experiments. Researchers discovered that strong Kondo coupling transforms the system into a Haldane spin-1 state, which couples to the metallic surface. This Haldane state, stabilized by incomplete screening of magnetic moments, exhibits topological edge modes and remains stable even with small changes in the system. The surrounding environment critically influences the system’s behaviour; coupling to a metal creates a significant effect, while a semi-metal has a negligible one at the system’s fundamental state.

The team discovered that the environment significantly influences the system’s response to external stimuli. Coupling to a metal results in a relevant perturbation, while a semi-metal leads to an irrelevant one at the decoupled fixed point. In the limit of large positive anisotropy, the system behaves like an anisotropic spin-Kondo system, and with large negative anisotropy, spins freeze in the Ising configuration. For small anisotropy, the metallic environment dominates the system’s behaviour. On semi-metallic surfaces, the Kondo coupling is irrelevant, leading to Kondo breakdown regardless of the anisotropy, whereas on metallic surfaces, the resulting dissipation induces antiferromagnetic ordering along the chain.

Notably, the research identifies a continuous transition separating the Kondo breakdown or dissipation-induced long-range ordered phases from the underscreened Haldane phase. These findings are supported by both scaling arguments and sign-free auxiliary-field Monte Carlo simulations, which demonstrate the system’s behaviour on semi-metals and reveal the emergence of long-range order on metals. The team also confirmed the existence of massless spin-1 edge modes and investigated the influence of varying single-ion anisotropy, establishing a foundation for exploring exotic phases of quantum matter in artificial spin lattices.

Chains Exhibit Topological Edge Modes on Surfaces

This research investigates the behaviour of magnetic chains, specifically, chains of cobalt atoms deposited on a surface, and reveals how their magnetic properties are influenced by the surrounding material. Scientists demonstrate that these chains exhibit a unique state arising from incomplete screening of their magnetic moments, leading to the emergence of topological edge modes, distinct states localized at the chain’s boundaries. The team discovered that the nature of the interaction between the chain and the surrounding material, whether a metal or a semi-metal, plays a crucial role in determining the chain’s overall magnetic order. Specifically, the research shows that on a semi-metallic surface, the chain’s magnetic coupling weakens, leading to a breakdown of the screening effect regardless of the strength of the interaction.

In contrast, on a metallic surface, the interaction induces long-range magnetic ordering along the chain. Through detailed analysis and simulations, the scientists identified a critical point where the system transitions between these different states, underscreened, dissipation-induced ordered, or Kondo breakdown, providing a comprehensive understanding of the interplay between topology, magnetism, and the electronic environment. This work advances fundamental knowledge of quantum magnetism and provides insights into the design of novel materials with tailored magnetic properties.