Theoretical Aspects of Mainly Low Dimensional Magnetic Systems

Veikko Halonen

George Mathew

A number of many-body problems that are highly complex in three dimensions can be solved in a low-dimensional system. Simple one-dimensional Hamiltonians that describe such systems have yielded exact, closed-form solutions for their dynamic and static properties. Low-dimensional magnets have gained significant attention for their distinct characteristics that facilitate the analysis of quantum model ground and excited states, the examination of potential new phases of matter, and exploration of the interplay between thermal and quantum fluctuations. The chapter’s main topic is theoretical ideas and outcomes concerning one-dimensional magnetism, and their relevance to real materials and experiments.

Hitoshi Asakawa, 浅川 仁

Daniel I. Khomskii

Aimed at graduate students and researchers, this book covers the key aspects of the modern quantum theory of solids, including up-to-date ideas such as quantum fluctuations and strong electron correlations. It presents in the main concepts of the modern quantum theory of solids, as well as a general description of the essential theoretical methods required when working with these systems. Diverse topics such as general theory of phase transitions, harmonic and anharmonic lattices, Bose condensation and superfluidity, modern aspects of magnetism including resonating valence bonds, electrons in metals, and strong electron correlations are treated using unifying concepts of order and elementary excitations. The main theoretical tools used to treat these problems are introduced and explained in a simple way, and their applications are demonstrated through concrete examples.

Peng Li

Indrani Bose

Quantum magnetism is one of the most active areas of research in condensed matter physics. There is significant research interest specially in low-dimensional quantum spin systems. Such systems have a large number of experimental realizations and exhibit a variety of phenomena the origin of which can be attributed to quantum effects and low dimensions. In this review, an overview of some aspects of quantum magnetism in low dimensions is given. The emphasis is on key concepts, theorems and rigorous results as well as models of spin chains, ladders and frustated magnetic systems.