The book introduces tools with which models of quantum matter are built. The most important technique, the Bethe ansatz, is developed in detail to perform exact calculations of the physical properties of quantum matter.

What is "topological" about topological quantum states? How many types of topological quantum phases are there? What is a zero-energy Majorana mode, how can it be realized in a solid state system, and how can it be used as a platform for topological quantum computation? What is quantum computation and what makes it different from classical computation? Addressing these and other related questions, Introduction to Topological Quantum Matter & Quantum Computation provides an introduction to and a synthesis of a fascinating and rapidly expanding research field emerging at the crossroads of condensed matter physics, mathematics, and computer science. Providing the big picture, this book is ideal for graduate students and researchers entering this field as it allows for the fruitful transfer of paradigms and ideas amongst different areas, and includes many specific examples to help the reader understand abstract and sometimes challenging concepts. It explores the topological quantum world beyond the well-known topological insulators and superconductors and emphasizes the deep connections with quantum computation. It addresses key principles behind the classification of topological quantum phases and relevant mathematical concepts and discusses models of interacting and noninteracting topological systems, such as the torric code and the p-wave superconductor. The book also covers the basic properties of anyons, and aspects concerning the realization of topological states in solid state structures and cold atom systems. Quantum computation is also presented using a broad perspective, which includes fundamental aspects of quantum mechanics, such as Bell's theorem, basic concepts in the theory of computation, such as computational models and computational complexity, examples of quantum algorithms, and elements of classical and quantum information theory.

A comprehensive overview of holographic methods in quantum matter, written by pioneers in the field. This book, written by pioneers in the field, offers a comprehensive overview of holographic methods in quantum matter. It covers influential developments in theoretical physics, making the key concepts accessible to researchers and students in both high energy and condensed matter physics. The book provides a unique combination of theoretical and historical context, technical results, extensive references to the literature, and exercises. It will give readers the ability to understand the important problems in the field, both those that have been solved and those that remain unsolved, and will enable them to engage directly with the current literature. The book describes a particular interface between condensed matter physics, gravitational physics, and string and quantum field theory made possible by holographic duality. The chapters cover such topics as the essential workings of the holographic correspondence; strongly interacting quantum matter at a fixed commensurate density; compressible quantum matter with a variable density; transport in quantum matter; the holographic description of symmetry broken phases; and the relevance of the topics covered to experimental challenges in specific quantum materials. Holographic Quantum Matter promises to be the definitive presentation of this material.

The Enrico Fermi summer school on Quantum Matter at Ultralow Temperatures held on 7-15 July 2014 at Varenna, Italy, featured important frontiers in the field of ultracold atoms. For the last 25 years, this field has undergone dramatic developments, which were chronicled by several Varenna summer schools, in 1991 on Laser Manipulation of Atoms, in 1998 on Bose-Einstein Condensation in Atomic Gases, and in 2006 on Ultra-cold Fermi Gases. The theme of the 2014 school demonstrates that the field has now branched out into many different directions, where the tools and precision of atomic physics are used to realise new quantum systems, or in other words, to quantum-engineer interesting Hamiltonians. The topics of the school identify major new directions: Quantum gases with long range interactions, either due to strong magnetic dipole forces, due to Rydberg excitations, or, for polar molecules, due to electric dipole interactions; quantum gases in lower dimensions; quantum gases with disorder; atoms in optical lattices, now with single-site optical resolution; systems with non-trivial topological properties, e.g. with spin-orbit coupling or in artificial gauge fields; quantum impurity problems (Bose and Fermi polarons); quantum magnetism. Fermi gases with strong interactions, spinor Bose-Einstein condensates and coupled multi-component Bose gases or Bose-Fermi mixtures continue to be active areas. The current status of several of these areas is systematically summarized in this volume.

In topological quantum materials, quantum effects emerge at macroscopic scales and are robust to continuous changes in a material’s state. This striking synergy between quantum and topological properties is of great interest for both fundamental research and emerging technologies, especially in the fields of electronics and quantum information. This edition of the book presents a wealth of topological quantum materials, bringing together burgeoning research from different areas: topological insulators, transition metal dichalcogenides, Weyl semimetals, and unconventional and topological superconductors. The realization of the application potential of topological quantum materials requires understanding their properties at a fundamental level. This brings us back to the discovery of topological phases of matter, which earned the Nobel Prize in Physics in 2016. This book explores the connection between pioneering work on topological phases of matter and a flurry of activity that followed. The topics covered include the quantum anomalous and spin Hall effects, emergent axion electrodynamics and topological magnetoelectric effects, Weyl nodes and surface Fermi arcs, weak antilocalization, induced triplet superconductivity, Majorana fermion modes, and the fractional Josephson effect.

Impurities, disorder or amorphous systems – ill-condensed matter – are mostly considered inconveniences in the study of materials, which is otherwise heavily based on idealized perfect crystals. The Kondo effect and the scaling theory of localization are among the fundamental and early discoveries which revealed the novelty hidden in impure or disordered systems. Recent advances in condensed matter physics have emphasized the role of topology, spin-orbit coupling, and certain discrete symmetries such as time reversal in many physical phenomena. These have irreversibly transformed the essential ideas and purview of condensed matter physics, both in theoretical and experimental directions. However, many of these recent developments and their implications are limited to, or by, ideas that pertain to clean systems. This thesis deals with various aspects of these new developments, but in the case of unclean systems. The author introduces new ideas such as amorphous topological insulators, fractalized metals and fractionalized spins.

This thesis focuses on the exploration of nontrivial spin dynamics in graphene-based devices and topological materials, using realistic theoretical models and state-of-the-art quantum transport methodologies. The main outcomes of this work are: (i) the analysis of the crossover from diffusive to ballistic spin transport regimes in ultraclean graphene nonlocal devices, and (ii) investigation of spin transport and spin dynamics phenomena (such as the (quantum) spin Hall effect) in novel topological materials, such as monolayer Weyl semimetals WeTe2 and MoTe2. Indeed, the ballistic spin transport results are key for further interpretation of ultraclean spintronic devices, and will enable extracting precise values of spin diffusion lengths in diffusive transport and guide experiments in the (quasi)ballistic regime. Furthermore, the thesis provides an in-depth theoretical interpretation of puzzling huge measured efficiencies of the spin Hall effect in MoTe2, as well as a prediction of a novel canted quantum spin Hall effect in WTe2 with spins pointing in the yz plane.

Despite a long tradition of sophisticated, creative materials synthesis among quantum materials researchers, a sense of broader community has been lacking. In initiating the Fundamentals of Quantum Materials Winter School held annually at the University of Maryland, we wanted to bring together the next generation of growers to learn techniques and pointers directly from senior scientists, and it turns out that we were not alone. The enthusiasm from both students and teachers has been both gratifying and invigorating. Four schools later, we can confidently say that physicists, chemists, and materials scientists, experimentalists and theorists alike, all want to know how to make a good sample. With this in mind, we asked our lecturers to record their most important ideas and share their expertise with a broader audience. This resource is a compilation of fundamental and practical guides on the modern methods of materials synthesis utilized by these experts. We hope that you enjoy reading their essential guidance and state-of-the-art techniques as you explore the Fundamentals of Quantum Materials.

This book offers a new approach to the long-standing problem of high-Tc copper-oxide superconductors. It has been demonstrated that starting from a strongly correlated Hamiltonian, even within the mean-field regime, the “competing orders” revealed by experiments can be achieved using numerical calculations. In the introduction, readers will find a brief review of the high-Tc problem and the unique challenges it poses, as well as a comparatively simple numerical approach, the renormalized mean-field theory (RMFT), which provides rich results detailed in the following chapters. With an additional phase picked up by the original Hamiltonian, some behaviors of interactive fermions under an external magnetic field, which have since been experimentally observed using cold atom techniques, are also highlighted.

Semiconductor nanostructures are ideal systems to tailor the physical properties via quantum effects, utilizing special growth techniques, self-assembling, wet chemical processes or lithographic tools in combination with tuneable external electric and magnetic fields. Such systems are called "Quantum Materials".The electronic, photonic, and phononic properties of these systems are governed by size quantization and discrete energy levels. The charging is controlled by the Coulomb blockade. The spin can be manipulated by the geometrical structure, external gates and by integrating hybrid ferromagnetic emitters.This book reviews sophisticated preparation methods for quantum materials based on III-V and II-VI semiconductors and a wide variety of experimental techniques for the investigation of these interesting systems. It highlights selected experiments and theoretical concepts and gives such a state-of-the-art overview about the wide field of physics and chemistry that can be studied in these systems.