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This book offers a theoretical description of topological matter in terms of effective field theories, and in particular topological field theories, focusing on two main topics: topological superconductors and topological insulators.Even though there is vast literature on these subjects, the book fills an important gap by providing a concise introduction to both topological order and symmetry-protected phases using a modern mathematical language, and developing the theoretical concepts by highlighting the physics and the physical properties of the systems. Further, it discusses in detail the topological interactions for topologically ordered matter, and the response to smooth external fields for symmetry protected matter. The book also covers more specialized topics that cannot be found elsewhere. Specifically, the response of superconductors to geometry, including the newly discovered geo-Meissner effect; and a correction to the usual Meissner effect, only present in the topologically interesting chiral superconductors.

This textbook introduces topological defects and solitons at a level suitable for advanced undergraduates and beginning graduate students in physics and materials science. It avoids the formal mathematics of topology, and instead concentrates on the physical properties of these topological structures. The first half of the book concentrates on fundamental principles of defects and solitons, and illustrates these principles with a single example—the xy model for 2D magnetic order. It begins by defining the concept of a winding number, and uses this concept to describe the topology of defects (vortices or disclinations) and solitons (domain walls), carefully identifying the similarities and differences between these two types of topological structures. It then goes on to discuss physical properties of defects and solitons, including free energy, dynamics, statistical mechanics, and coupling with curvature. It shows how these concepts emerge from a theory with variable magnitude of order, and hence how topology can be viewed as an approximation to physics. The second half goes on to explore a wider range of topological defects and solitons. First, it considers more complex types of order—2D nematic liquid crystals, 3D magnetic or liquid-crystal order, 2D or 3D crystalline solids—and shows how each type of order leads to specific topological structures. Next, it discusses defects and solitons that are characterized by 2D or 3D measuring surfaces, not just 1D loops, including hedgehogs, skyrmions, and hopfions. These structures are more complex, but they can still be understood using the same fundamental principles. A final chapter describes the formation of phases with regular arrays of defects or solitons.

This open access book presents a comprehensive exploration of diffusion metamaterials that control energy and mass diffusion. Currently, if from the perspective of governing equations, diffusion metamaterials and wave metamaterials (pioneered by J. B. Pendry in the 1990s) are recognised as the two most prominent branches in the field of metamaterials. These two branches differ in their emphasis on the diffusion equation (as the governing equation) and time-dependent characteristic lengths in diffusion metamaterials, as opposed to the wave equation (as the governing equation) and time-independent characteristic lengths in wave metamaterials. Organized into three distinct parts –'Thermal Diffusion Metamaterials','Particle Diffusion Metamaterials', and'Plasma Diffusion Metamaterials'– this book offers a rigorous exploration spanning physics, engineering, and materials science, aimed at advancing our understanding of diffusion processes controlled by diffusion metamaterials. Incorporating foundational theory, computational simulations, and laboratory experiments, the book equips researchers and scholars across these disciplines with comprehensive methods, insights, and results pivotal to the advancement of diffusion control. Beyond facilitating interdisciplinary discourse, the book serves as a catalyst for innovative breakthroughs at the crossroads of physics, thermodynamics, and materials science. Essentially, readers will acquire profound insights that empower them to spearhead advancements in diffusion science (diffusionics) and the engineering of metamaterials.

This comprehensive book delves into the fascinating world of quasiparticle properties of graphene-related materials. The authors thoroughly explore the intricate effects of intrinsic and extrinsic interactions on the material's properties, while unifying the single-particle and many-particle properties through the development of a theoretical framework. The book covers a wide range of research topics, including long-range Coulomb interactions, dynamic charge density waves, Friedel oscillations and plasmon excitations, as well as optical reflection and transmission spectra of thin films. Also it highlights the crucial roles of inelastic Coulomb scattering and optical scattering in the quasiparticle properties of layered systems, and the impact of crystal symmetry, number of layers, and stacking configuration on their uniqueness. Furthermore, the authors explore the topological properties of quasiparticles, including 2D time-reversal-symmetry protected topological insulators with quantum spin Hall effect, and rhombohedral graphite with Dirac nodal lines. Meanwhile, the book examines the gate potential application for creating topological localized states and shows topological invariants of 2D Dirac fermions, and binary Z2 topological invariants under chiral symmetry. The calculated results are consistent with the present experimental observations, establishing it as a valuable resource for individuals interested in the quasiparticle properties of novel materials.

This thesis provides an in-depth investigation of effective non-Hermiticity and topology in many-mode, non-interacting, bosonic systems. It also establishes the extent to which one must move beyond the Hamiltonian, closed-system setting, in order to uncover signatures of genuine symmetry-protected topological (SPT) physics in'free'(mean-field) bosons. While SPT phases of free fermionic matter and their associated zero-energy boundary-localized modes have been thoroughly explored, similar physics in free bosonic systems still remains elusive. No fermionic counterpart exists for the distinctive dynamical behavior that arises from the effective non-Hermiticity, intrinsic even at equilibrium, to bosonic Hamiltonians. Therefore, a much needed paradigm shift is required to address major conceptual roadblocks in the search for SPT bosonic phases.The analysis within develops, in particular, the notion of topological metastability in quadratic bosonic systems subject to Markovian dissipation. The resulting dynamical paradigm was found to be characterized by both a sharp separation between transient and asymptotic dynamics and non-trivial topological invariants. It also features long-lived boundary-localized'Majorana boson'and'Dirac boson'modes, which realize tight bosonic analogues to the edge modes characteristic of fermionic SPT phases. This comprehensive look into non-interacting bosonic systems breaks important new ground for re-imagining quantum phenomena beyond equilibrium, with novel applications in quantum science.

The book offers a pedagogical introduction to higher-spin gauge theories. These theories build upon fundamental gauge theories that are crucial for understanding core interactions. Electromagnetism and nuclear forces are associated with gauge fields of spin 1, while gravity can be conceptualized as a gauge theory of spin 2. This prompts the intriguing inquiry: do higher-spin gauge theories exist? Such theories would extend gravity, incorporating massless gauge fields of spins higher than two. They appear to bear connections to string theory and offer a captivating framework for exploring gravity and aspects of quantum gravity. The book initiates with a primer offering a comprehensive discussion on higher spins, delving into the challenges of establishing coherent interactions. It then explores methodologies to surmount these challenges within three-dimensional space-time. Furthermore, it investigates the emergence of asymptotic symmetry algebras, establishing links to a holographic dual conformal theory. The final chapter introduces Vasiliev's approach to higher-spin gauge theory in four dimensions. Designed for advanced students and young researchers in theoretical physics and mathematical physics, the book aims to elucidate fundamental ideas, concepts, and tools underpinning higher-spin gauge theories. The inclusion of numerous exercises complements and illustrates the content, preparing readers for engagement with the subject's original literature and ongoing developments. To fully engage with the book's arguments, a prerequisite understanding of field theories and conventional gauge theories, including gravity, is assumed.

The book is mainly designed for post-graduate students to learn modern-day condensed matter physics. While emphasizing an experiment called the ‘Quantum Hall effect', it introduces the subject of'Topology'and how the topological invariants are related to the quantization of the Hall plateaus. Thus, the content tries to deliver an account of the topological aspects of materials that have shaped the study of condensed matter physics in recent times. The subject is often quite involved for a student to grasp the fundamentals and relate them to physical phenomena. Further, these topics are mostly left out of the undergraduate curriculum, although they often require a simplistic view of the concepts involved to be presented pedagogically. The book contains examples, worked-out concepts, important derivations, diagrams for illustration, etc. to aid the understanding of the students. The book also emphasizes the experimental discoveries that put the subject in its perspective and elaborate on the applications which are likely to be of interest to scientists and engineers.

Ever since 1911, the Solvay Conferences have shaped modern physics. The format is quite different from other conferences as the emphasis is placed on discussion. The 28th edition held in May 2022 in Brussels and chaired by David Gross and Peter Zoller continued this tradition and addressed some of the most pressing open questions in the fields of quantum information, gathering many of the leading figures working on a wide variety of profound problems.The proceedings contain the'rapporteur talks'giving a broad overview with unique insights by distinguished renowned scientists. These lectures cover the five sessions: The Physics of Quantum Information, Many-Body Entanglement, Quantum Information and Spacetime, Quantum Platforms, Quantum Algorithms.In the Solvay tradition, the proceedings also include the prepared comments to the rapporteur talks. The discussions among the participants — expert, yet lively and sometimes contentious — have been edited to retain their flavor and are reproduced in full. The reader is taken on a breathtaking ride through a fascinating field which is expanding rapidly.

A P Balachandran has a long and impressive record of research in particle physics and quantum field theory, bringing concepts of geometry, topology and operator algebras to the analysis of physical problems, particularly in particle physics and condensed matter physics. He has also had an influential role within the physics community, not only in terms of a large number of students, research associates and collaborators, but also serving on the editorial boards of important publications, including the International Journal of Modern Physics A.This book consists of articles by students and associates of Balachandran. Most of the articles are scientific in nature, with topics ranging from noncommutative geometry, particle physics phenomenology, to condensed matter physics. Various chapters focus on new perspectives and directions resulting from Balachandran's contributions to physics, as well as some reminiscences of collaborating and working with Balachandran.

Dieses Buch beschreibt die erstmalige, erfolgreiche Realisierung unkonventioneller Superfluide in höheren Bändern des hexagonalen optischen Gitters. Der Populationstransfer und der anschließende dynamische Quantenphasenübergang werden ausführlich diskutiert. Schließlich werden die Metastabilität und Zerfallskanäle des ultrakalten Systems experimentell nachgewiesen. Durch die Reduktion von Phasenrauschen des optischen Gitters konnte die Lebensdauer des ultrakalten Ensembles um etwa eine Größenordnung erhöht werden. Weiterhin werden die optische Phasenregelschleife und Intensitätsstabilisierung des Gitters vorgestellt. Mit den in diesem Buch beschriebenen Ergebnissen und technologischen Entwicklungen werden die derzeit bestehenden Grenzen der Quantensimulation mittels ultrakalter Gase in optischen Gittern aufgehoben und der Weg für zahlreiche nachfolgende Untersuchungen bereitet.

This book covers recent developments in the understanding, quantification, and exploitation of entanglement in spin chain models from both condensed matter and quantum information perspectives. Spin chain models are at the foundation of condensed matter physics and quantum information technologies and elucidate many fundamental phenomena such as information scrambling, quantum phase transitions, and many-body localization. Moreover, many quantum materials and emerging quantum devices are well described by spin chains. Comprising accessible, self-contained chapters written by leading researchers, this book is essential reading for graduate students and researchers in quantum materials and quantum information. The coverage is comprehensive, from the fundamental entanglement aspects of quantum criticality, non-equilibrium dynamics, classical and quantum simulation of spin chains through to their experimental realizations, and beyond into machine learning applications.

The Handbook of Materials Modeling, 2nd edition is a six-volume major reference serving a steadily growing community at the intersection of two mainstreams of global research: computational science and materials science and technology. This extensively expanded new edition reflects the significant developments in all aspects of computational materials research over the past decade, featuring progress in simulations at multiple scales and increasingly more realistic materials models. Thematically separated into two mutually dependent sets – “Methods: Theory and Modeling (MTM)” and “Applications: Current and Emerging Materials (ACE)” – the handbook runs the entire gamut from theory and methods to simulations and applications. Readers benefit from its in-depth coverage of a broad methodological spectrum extending from advanced atomistic simulations of rare events to data-driven artificial intelligence strategies for materials informatics in the set MTM, as well as forefront emphasis onmaterials of far-ranging societal importance such as photovoltaics and energy-relevant oxides, and cutting-edge applications to materials for spintronic devices, graphene, cement, and glasses in the set ACE. The thorough, interconnected coverage of methods and applications, together with a line-up of internationally acclaimed editors and authors, will ensure the Handbook of Material Modeling's standing as an enduring source of learning and inspiration for a global community of computational materials scientists.

This book presents a selection of advanced lectures from leading researchers, providing recent theoretical results on strongly coupled quantum field theories. It also analyzes their use for describing new quantum states, which are physically realizable in condensed matter, cold-atomic systems, as well as artificial materials. It particularly focuses on the engineering of these states in quantum devices and novel materials useful for quantum information processing. The book offers graduate students and young researchers in the field of modern condensed matter theory an updated review of the most relevant theoretical methods used in strongly coupled field theory and string theory. It also provides the tools for understanding their relevance in describing the emergence of new quantum states in a variety of physical settings. Specifically, this proceedings book summarizes new and previously unrelated developments in modern condensed matter physics, in particular: the interface of condensed matter theory and quantum information theory; the interface of condensed matter physics and the mathematics emerging from the classification of the topological phases of matter, such as topological insulators and topological superconductors; and the simulation of condensed matter systems with cold atoms in optical lattices.

This proceedings is based on the interdisciplinary workshop held in Madrid, 5-9 March 2018, dedicated to Alberto Ibort on his 60th birthday. Alberto has great and significantly contributed to many fields of mathematics and physics, always with highly original and innovative ideas.Most of Albertos's scientific activity has been motivated by geometric ideas, concepts and tools that are deeply related to the framework of classical dynamics and quantum mechanics.Let us mention some of the fields of expertise of Alberto Ibort:Geometric Mechanics; Constrained Systems; Variational Principles; Multisymplectic structures for field theories; Super manifolds; Inverse problem for Bosonic and Fermionic systems; Quantum Groups, Integrable systems, BRST Symmetries; Implicit differential equations; Yang-Mills Theories; BiHamiltonian Systems; Topology Change and Quantum Boundary Conditions; Classical and Quantum Control; Orthogonal Polynomials; Quantum Field Theory and Noncommutative Spaces; Classical and Quantum Tomography; Quantum Mechanics on phase space; Wigner-Weyl formalism; Lie-Jordan Algebras, Classical and Quantum; Quantum-to-Classical transition; Contraction of Associative Algebras; contact geometry, among many others.In each contribution, one may find not only technical novelties but also completely new way of looking at the considered problems. Even an experienced reader, reading Alberto's contributions on his field of expertise, will find new perspectives on the considered topic.His enthusiasm is happily contagious, for this reason he has had, and still has, very bright students wishing to elaborate their PhD thesis under his guidance.What is more impressive, is the broad list of rather different topics on which he has contributed.

Geometry and topology have been a fascination in physics since the start of the 20th century. A leading example is Einstein's geometrical theory of gravity. At the beginning of the 1970s, topological ideas entered areas of condensed matter physics. These advances were driven by new seminal ideas resolving a serious contradiction between experiment and the standard interpretation of a rigorous mathematical theorem which led to the study of new exotic topological phases of matter. Topological defect driven phase transitions in thin, two dimensional films of superfluids, superconductors and crystals have provided great insight into the mechanism governing these topological phases present in those physical systems. Moreover, many of these topological properties remain'protected'against disorder and topological distortion perturbations. An example of possible applications of such robustness to perturbations is in the search for encoding information in quantum computers, potentially providing the platform for fault-tolerant quantum computations.In the past four decades, the discovery of topological phases engendered great interest in condensed matter physics. It also attracted the attention of researchers working on quantum information, quantum materials and simulations, high energy physics and string theory. This unique volume contains articles written by some of the most prominent names in the field, including Nobel Laureate John Michael Kosterlitz and Professor Jorge V José. They originate from talks and discussions by leading experts at a recent workshop. They review previous works as well as addressing contemporary developments in the most pressing and important issues on various aspects of topological phases and topological phase transitions.

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 book collects various perspectives, contributed by both mathematicians and physicists, on the B-model and its role in mirror symmetry. Mirror symmetry is an active topic of research in both the mathematics and physics communities, but among mathematicians, the “A-model” half of the story remains much better-understood than the B-model. This book aims to address that imbalance. It begins with an overview of several methods by which mirrors have been constructed, and from there, gives a thorough account of the “BCOV” B-model theory from a physical perspective; this includes the appearance of such phenomena as the holomorphic anomaly equation and connections to number theory via modularity. Following a mathematical exposition of the subject of quantization, the remainder of the book is devoted to the B-model from a mathematician's point-of-view, including such topics as polyvector fields and primitive forms, Givental's ancestor potential, and integrablesystems.

The book addresses several aspects of thermodynamics and correlations in the strongly-interacting regime of one-dimensional bosons, a topic at the forefront of current theoretical and experimental studies. Strongly correlated systems of one-dimensional bosons have a long history of theoretical study. Their experimental realisation in ultracold atom experiments is the subject of current research, which took off in the early 2000s. Yet these experiments raise new theoretical questions, just begging to be answered. Correlation functions are readily available for experimental measurements. In this book, they are tackled by means of sophisticated theoretical methods developed in condensed matter physics and mathematical physics, such as bosonization, the Bethe Ansatz and conformal field theory. Readers are introduced to these techniques, which are subsequently used to investigate many-body static and dynamical correlation functions.

Many open questions in Theoretical Physics pertain to strongly interacting quantum systems such as the quark-gluon plasma (QGP) produced in heavy-ion collisions or the strange-metal phase observed in many high-temperature superconductors. These systems are notoriously difficult to study using traditional methods such as perturbation theory, but the gauge/gravity duality offers a successful alternative approach, which maps strongly interacting quantum gauge theories to computationally tractable, classical gravity theories. This book begins with a pedagogical introduction to how the duality can be used to extract transport properties of quantum systems from their gravity dual. It then presents new results on hydrodynamic transport in strongly interacting quantum fluids, providing strong evidence that the Haack-Yarom identity between second-order transport coefficients holds for all fluids with a classical gravity dual and may be a universal feature of all strongly coupled quantum fluids such as the QGP. Newly derived Kubo formulae, expressing transport coefficients in terms of quantum correlators, hold independently of the duality. Lastly, the book discusses new results on magnetic impurities in strongly correlated metals, including the first dual gravity description of an inter-impurity coupling, crucial for the quantum criticality underlying the strange-metal phase.