Colloquium: Atomic spin chains on surfaces

Low-dimensional physical systems are characterized by unusual behavior due to strong quantum fluctuations and electron-electron interactions which arise from the confinement of electrons. The capability of tuning interactions and geometry of one-dimensional (1D) systems is an opportunity to test the limits of quantum systems. In this Colloquium the physics of 1D spin chains on surfaces is discussed from the experimental and theoretical points of view. Also discussed are the opportunities in emerging areas of research such as quantum computation and communication and spintronics.