Among his many important contributions to condensed matter physics, Igor Dzyaloshinskii published several seminal papers which contributed essentially to our understanding of the unusual behaviour of one-dimensional electronic systems. In this review I will briefly outline the main results obtained mostly in two of them and will present further developments in this field.
Among his many important contributions to condensed matter physics, Igor Dzyaloshinskii published several seminal papers which contributed essentially to our understanding of the unusual behaviour of one-dimensional electronic systems. In this review I will briefly outline the main results obtained mostly in two of them and will present further developments in this field.
To a casual ostrich the world of quantum physics in one dimension may sound a little one-dimensional, suitable perhaps for those with an unhealthy obsession for the esoteric. Nothing of course could be further from the truth. The field is remarkably rich and broad, and for more than fifty years has thrown up innumerable challenges. Theorists, realising that the role of interactions in 1D is special and that well known paradigms of higher dimensions (Fermi liquid theory for example) no longer apply, took up the challenge of developing new concepts and techniques to understand the undoubted pecularities of one-dimensional systems. And experimentalists have succeeded in turning pipe dreams into reality, producing an impressive and ever increasing array of experimental realizations of 1D systems, from the molecular to the mesoscopic---spin and ladder compounds, organic superconductors, carbon nanotubes, quantum wires, Josephson junction arrays and so on. Many books on the theory of one-dimensional systems are however written by experts for experts, and tend as such to leave the non-specialist a touch bewildered. This is understandable on both fronts, for the underlying theoretical techniques are unquestionably sophisticated and not usually part of standard courses in many-body theory. A brave author it is then who aims to produce a well rounded, if necessarily partial, overview of quantum physics in one dimension, accessible to a beginner yet taking them to the edge of current research, and providing en route a thorough grounding in the fundamental ideas, basic methods and essential phenomenology of the field. It is of course the brave who succeed in this world, and Thierry Giamarchi does just that with this excellent book, written by an expert for the uninitiated. Aimed in particular at graduate students in theoretical condensed matter physics, and assumimg little theoretical background on the part of the reader (well just a little), Giamarchi writes in a refreshingly relaxed style with infectious enthusiasm for his subject, and readily combines formal instruction with physical insight. The result is a serious, pedagogical yet comprehensive guide to the fascinating and important field of one-dimensional quantum systems, for which many a graduate student (and not a few oldies) will be grateful. The first half of the book, chapters 1--5, is devoted to a coherent presentation of the essential concepts and theoretical methods of the field. After a basic introduction to the unique behaviour of interacting electrons in one dimension, and to early fermionic approaches to the problem, Giamarchi turns to the technique of bosonization, introducing chapter 3 with a Marxist quote: `A child of five would understand this. Send for a child of five.' This most powerful technique is presented in a step by step fashion, and serious perusal of the chapter will benefit all ages since bosonization is used extensively throughout the rest of the book. The same is true of chapter 3 where a phenomenological and physically insightful introduction is given to the Luttinger liquid---the key concept in the low-energy physics of one-dimensional systems, analogous to the Fermi liquid in higher dimensions. Chapter 4 deals with what the author calls `refinements', or complications of the sort theorists in particular welcome; such as how the Luttinger liquid description is modified by the presence of long-ranged interactions, the Mott transition (`we forgot the lattice Gromit'), and the effects of breaking spin rotational invariance on application of a magnetic field. Finally chapter 5 describes various microscopic methods for one dimension, including a brief discussion of numerical techniques but focussing primarily on the Bethe ansatz---the famous one-dimensional technique others seek to emulate but whose well known complexity necessitates a relatively brief discussion, confined in practice to the spin-1/2 Heisenberg model. In the second half of the book, chapters 6--11, a range of different physical realizations of one-dimensional quantum physics are discussed. According to taste and interest, these chapters can be read in essentially any order. Spin systems are considered in chapter 6, beginning with spin chains---Jordan--Wigner, the bosonization solution---before moving to frustration, the spin-Peierls transition, and spin ladders; and including experimental examples of both spin chain and ladder materials. Chapters 7 and 8 deal with interacting lattice fermions, the former with single chain problems, notably the Hubbard, t-J and related models; and the latter with coupled fermionic chains, from finite to infinite, including a fulsome discussion of Bechgaard salts (organic conductors) as exemplars of Luttinger liquid behaviour. The effect of disorder in fermionic systems is taken up in chapter 9, and here the reader may react: interacting systems are tough enough, why make life harder? But disorder is always present to some degree in real systems---quantum wires, for example, discussed briefly in the chapter---and its effects particularly acute in one dimension. It simply cannot be avoided, even if the problem of interacting, disordered one-dimensional systems is still a long way off being solved. The penultimate chapter deals with the topical issues of boundaries, isolated impurities and constrictions, with a primary focus on mesoscopic examples of Luttinger liquids, notably carbon nanotubes and edge states in the quantum Hall effect. Finally `significant other' examples of Luttinger liquids, namely interacting one-dimensional bosons, are considered in chapter 11; which concludes with a discussion of bosonization techniques in the context of quantum impurities in Fermi liquids---the x-ray, Kondo and multichannel Kondo problems. The quality of the product attests to the fact that writing this impressive tome was a labour of love for the author. Anyone with a serious interest in getting to grips with one-dimensional quantum systems simply needs the book on their shelves---and will have great fun reading it too.
The electron liquid paradigm is at the basis of most of our current understanding of the physical properties of electronic systems. Quite remarkably, the latter are nowadays at the intersection of the most exciting areas of science: materials science, quantum chemistry, nano-electronics, biology, and quantum computation. Accordingly, its importance can hardly be overestimated. During the past 20 years the field has witnessed momentous developments, which are partly covered in this new volume. Advances in semiconductor technology have allowed the realizations of ultra-pure electron liquids whose density, unlike that of the ones spontaneously occurring in nature, can be tuned by electrical means, allowing a systematic exploration of both strongly and weakly correlated regimes. Most of these system are two- or even one-dimensional, and can be coupled together in the form of multi-layers or multi-wires, opening vast observational possibilities. On the theoretical side, quantum Monte Carlo methods have allowed an essentially exact determination of the ground-state energy of the electron liquid, and have provided partial answers to the still open question of the structure of its phase diagram. Starting from the 1980s some truly revolutionary concepts have emerged, which are well represented in this volume.
This paper presents a brief introduction to some of the systems and questions concerning one-dimensional interacting quantum systems. Historically, organic conductors and superconductors – a field extremely active in the “Laboratoire de physique des solides” in Orsay, in a good part thanks to the influence of Jacques Friedel, played a crucial role in this field. I will describe some of the aspects of this physics and also review some of the very exciting theoretical and experimental developments that took place in the 1D world in the last 15 years or so.
In this review, the importance of the Dzyaloshinskii-Moriya Interaction (DMI) to the magnetic properties of quantum spin systems is discussed mainly focusing on the determination of or understanding the role of DMI extracted from highfrequency high-field electron spin resonance (ESR) measurements.This review includes the ESR theories of the S = 1=2 one-dimensional (1D) antiferromagnet with the staggered field (Oshikawa-Affleck theory) and with the uniform DMI, and several related experimental results are shown.Then, the proposed mechanisms of the singlet-triplet transition in quantum spin systems together with the ESR selection rules are introduced in connection with various experimental results.Finally, the role of DMI in the ground state of kagome lattice antiferromagnets and the honeycomb lattice antiferromagnet is discussed with some experimental results.
conferred him PhD degree after successful defense of PhD thesis entitled "Statistical theory of partially excited systems", which Oleg elaborated under the guidance of Professor Ihor Yukhnovskii and Professor Roman Levitskii.Over the past few decades Oleg Derzhko has been scientifically working at the Institute for Condensed Matter Physics of National Academy of Sciences of Ukraine in Lviv, at first, as a research associate at the former Lviv Division of the Institute for Theoretical Physics of the Academy of Sciences of the UkrSSR (since 1982), and finally as head of Department for Theory of Model Spin Systems (2003-2016) and head of Department for Quantum Statistics (since 2016 up till now).During this period, he has also performed a long-term lecturing of several courses of theoretical physics at Ivan Franko National University in Lviv and Lviv Polytechnic National University.Oleg's scientific interests cover various modern problems of condensed matter physics and statistical physics.At the Institute for Condensed Matter Physics in Lviv OlegDerzhko has successfully developed a research direction, which is primarily focused on the state-of-theart problems of quantum spin models with a particular emphasis on the exactly solvable models and is already recognized worldwide.In addition to this challenging research topic in its own right, Oleg has a lot of other scientific interests including, but not limited to, unsolved problems of phase transitions of atomic liquids.It is impossible to summarize here all Oleg's achievements, so let us briefly review at least a few most important milestones of his scientific career.Early-career scientific contributions of Oleg Derzhko were devoted to equilibrium properties of partially excited gas and an influence of resonance irradiation upon a liquid-gas phase transition [1].He did not stop taking interest in this topic across his entire scientific career.The further research in this direction has been developing mainly in collaboration with Dr. Vasyl Myhal where their joint efforts are focused on the properties of a two-phase fluid of two-level atoms, the part of which is excited.Among other matters, Oleg and Vasyl brought a deeper understanding into the vapor-to-liquid transition, wetting under electromagnetic resonance irradiation, a microscopic theory of photonucleation with the special emphasis laid on nucleation phenomena in an electric field, surface tension, cavitation and so on [2][3][4].Exactly solvable problems in general and particularly one-dimensional quantum XY models and quantum Ising models in a transverse magnetic field have apparently become Oleg's greatest scientific passion and delight, where he substantially extended the rigorous results with the help of Jordan-Wigner fermionization technique [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19].To this end, Oleg Derzhko and his collaborators, which were predominantly from the Institute for Condensed Matter Physics in Lviv, have nontrivially adapted the recipé originally envisaged in a seminal paper by Lieb, Schultz, and Mattis [20].A big step forward at that time was the formulation of the exact numerical method for the calculation of time-dependent spin correlation functions and the corresponding structure factors [5][6][7].Exact solutions for numerous random and periodic non-uniform versions of quantum XY and Ising models achieved by Oleg and by his research group brought a considerable progress in theoretical understanding of a lot of exciting phenomena emergent in one-dimensional quantum spin chains.For instance, in this field of study Oleg has significantly contributed to a clarification of the effect of regular nonuniformity, randomness and correlated disorder on static and dynamical properties of several exactly solved quantum XY and Ising chains [8][9][10][11][12][13][14].Oleg achieved another important breakthrough in this research area by a detailed examination of spin-Peierls instabilities of a certain class of quantum XY chains [15][16][17], as well as, quantum phase transitions and the dynamics of exactly solved XY chains with three-site interactions [16,18,19].
Driven by breakthroughs in experimental and theoretical techniques, the study of nonequilibrium quantum physics is a rapidly expanding field with many exciting new developments. Among the manifold ways the topic can be investigated, one-dimensional systems provide a particularly fine platform. The trifecta of strongly correlated physics, powerful theoretical techniques, and experimental viability have resulted in a flurry of research activity over the past decade or so. In this review, we explore the nonequilibrium aspects of one-dimensional systems that are integrable. Through a number of illustrative examples, we discuss nonequilibrium phenomena that arise in such models, the role played by integrability, and the consequences these have for more generic systems.