Exploring quantum phases in frustrated spin-1/2 chain and ladders: a detailed review

In this topical review, we explore low-dimensional spin-$\frac{1}{2}$ systems, focusing on key models such as the Majumdar-Ghosh (MG) model on a spin-$\frac{1}{2}$ chain and the Heisenberg spin-$\frac{1}{2}$ model applied to various ladder geometries, including normal, zigzag, two-leg honeycomb, skewed, and diamond. We discuss the key physical features and experimental realizations of these models in real materials, providing a detailed overview. The review also includes the Kitaev-Heisenberg model on a two-leg ladder, a recent development in quantum magnetism. It discusses emerging quantum phases, such as spin liquids and magnetization plateaus, and highlights open research areas, including the investigation of unexplored exotic ground states. Additionally, we briefly discuss how quantum simulators based on ion traps, superconducting circuits, optical lattices, etc., are being used as powerful tools to explore the ground-state phases of spin-$\frac{1}{2}$ systems. Furthermore, the review emphasizes the potential for new material design, offering an exciting avenue for future experimental and theoretical advancements in low-dimensional quantum systems.