A collection of local magnetic moments arranged in a linear fashion that interact via some spin-spin coupling is generally known as a **spin chain**. This seemingly simple object is one of the most complex and rich physical systems that have been studied since the advent of quantum mechanics without a decline in interest ever since. From the emulation of one-dimensional (1D) quantum phases to the potential realization of Majorana edge states, spin chains are unique systems to study.

As early as 1928, Werner Heisenberg explained ferromagnetism using Pauli’s exclusion principle and the interaction between spins that bears his name. Subsequently, antiferromagnetism was addressed in spin chains by the seminal works of Bethe and Hulthén.

In recent times the interest in spin chains continues. The 2016 Nobel Prize explicitly mentioned spin chains through the work of Haldane that revolutionized the understanding of condensed-matter physics by finding new phases of matter associated with a certain set of the two interactions defining the spin-chain parameters. Additionally, the study of spin chains has been instrumental in ushering the far-reaching concepts of topology in condensed matter.

The simplicity of spin chains as compared to three-dimensional systems brings in new phenomena proper to lower dimensions. One of them is the absence of long-range order. A related consequence is that phase transitions in 1D systems take place only at zero kelvin. Furthermore, correlations are enhanced at 1D. As a consequence, many-body physics is ubiquitous in 1D systems.

While the initial interest in spin chains was primarily from a theoretical viewpoint, various ways exist to create physical realizations of spin chains in either solids, trapped atoms, or molecules. Particularly, the development of the scanning tunneling microscope (STM) has furthered permitted to create spin chains on solid surfaces with atomic precision. And a great deal of progress in the experimental investigation of the physics of spin chains has been achieved through the development of quantum simulators based on atomic traps.

Now, a team of researchers reviews ^{1} the current state of research on spin correlations and dynamics of atomic spin chains as studied by the STM. They show an overview of entanglement, correlation, and decoherence – properties inherent to spin chains – in different contexts.

Complementary to other techniques such as atom traps or molecular crystals, the STM manipulation of atoms on surfaces offers an extremely controlled way of creating structures with tailored properties. The substrate is the main constraint in these systems, which, on the one hand, gives to environmental perturbations on the properties of the spin chain. On the other hand, the use of substrates makes it possible to eventually encapsulate and create devices, giving us ideas on how to create a useful technology out of the quantum properties of entangled spins.

The studies reviewed focus on the connection between spin chains and very promising technological possibilities. Namely, using spin instead of charge in solid-state devices (**spintronics**); information transmission with high fidelity (**quantum communication**); decoupling the spins to have access to qubits and operations on qubits within the quantum coherence time with the STM (**quantum computing**); spins on surfaces used to get experimentally the solutions to model Hamiltonians that represent the behavior of matter on the very-low-temperature scale (**quantum simulations**); atomic spins can be used as extremely precise and sensitive sensors (**quantum sensors**).

Recent advances have enabled researchers to measure lifetimes and coherence times of spins on surfaces with unprecedented accuracy. We are gathering new insight into the dynamics of superposition states and interactions at play. New phases of matter can now be explored, particularly the newly discovered topological phases. Spin-chain research is a thriving field right now.

*Author: César Tomé López is a science writer and the editor of Mapping Ignorance*

*Disclaimer: Parts of this article may have been copied verbatim or almost verbatim from the referenced research paper.*

## References

- Deung-Jang Choi, Nicolas Lorente, Jens Wiebe, Kirsten von Bergmann, Alexander F. Otte, and Andreas J. Heinrich (2019) Colloquium: Atomic spin chains on surfaces reviews of Modern Physics doi: 10.1103/RevModPhys.91.041001 ↩