Strongly Interacting Quantum Systems Volume 2 Many Body Physics

This book studies the fundamental aspects of many-body physics in quantum systems open to an external world. Recent remarkable developments in the observation and manipulation of quantum matter at the single-quantum level point to a new research area of open many-body systems, where interactions with an external observer and the environment play a major role. The first part of the book elucidates the influence of measurement backaction from an external observer, revealing new types of quantum critical phenomena and out-of-equilibrium dynamics beyond the conventional paradigm of closed systems. In turn, the second part develops a powerful theoretical approach to study the in- and out-of-equilibrium physics of an open quantum system strongly correlated with an external environment, where the entanglement between the system and the environment plays an essential role. The results obtained here offer essential theoretical results for understanding the many-body physics of quantum systems open to an external world, and can be applied to experimental systems in atomic, molecular and optical physics, quantum information science and condensed matter physics.

In the excitement and rapid pace of developments, writing pedagogical texts has low priority for most researchers. However, in transforming my lecture l notes into this book, I found a personal benefit: the organization of what I understand in a (hopefully simple) logical sequence. Very little in this text is my original contribution. Most of the knowledge was collected from the research literature. Some was acquired by conversations with colleagues; a kind of physics oral tradition passed between disciples of a similar faith. For many years, diagramatic perturbation theory has been the major theoretical tool for treating interactions in metals, semiconductors, itiner ant magnets, and superconductors. It is in essence a weak coupling expan sion about free quasiparticles. Many experimental discoveries during the last decade, including heavy fermions, fractional quantum Hall effect, high temperature superconductivity, and quantum spin chains, are not readily accessible from the weak coupling point of view. Therefore, recent years have seen vigorous development of alternative, nonperturbative tools for handling strong electron-electron interactions. I concentrate on two basic paradigms of strongly interacting (or con strained) quantum systems: the Hubbard model and the Heisenberg model. These models are vehicles for fundamental concepts, such as effective Ha miltonians, variational ground states, spontaneous symmetry breaking, and quantum disorder. In addition, they are used as test grounds for various nonperturbative approximation schemes that have found applications in diverse areas of theoretical physics.

"Unabridged republication of the second edition of the work, originally published in the Pure and applied physics series by Academic Press, Inc., New York, in 1972"--Title page verso.

This book presents new experimental tools and theoretical concepts of collective nonequilibrium behavior of quantum systems. The book is based on the Les Houches Summer School of August 2012, "Strongly interacting quantum systems out of equilibrium".

The book is an introduction to quantum field theory applied to condensed matter physics. The topics cover modern applications in electron systems and electronic properties of mesoscopic systems and nanosystems. The textbook is developed for a graduate or advanced undergraduate course with exercises which aim at giving students the ability to confront real problems.

Strongly correlated electron systems are one of the central topics of condensed matter physics. The myriad of combinations of diverse Fermiologies, phonon spectra and electron-electron, electron-phonon interactions, together with spin-orbit couplings, Kondo couplings, and effects of disorder and external magnetic fields, leads to a truly dazzling range of quantum many-body phenomena. Superconductivity (conventional and unconventional) and magnetism are among the most prominent examples of quantum phases of matter that occur in such systems. We know that powerful emergent principles such as symmetry and topology are required to explain these emergent phenomena. However, due to the inherent difficulty of studying systems with macroscopically large number of strongly interacting particles, there remains the challenge of connecting these somewhat abstract mathematical principles with the underlying microscopic interactions. In this thesis, we illustrate, through two examples of systems with electron-electron and electron-phonon interactions, how one can simplify intractable quantum chemistry problems by reducing them to effective model Hamiltonians that capture the essence of microscopic interactions important to low-energy excitations, which we can then study using a variety of tools, such as determinantal quantum Monte Carlo (DQMC), exact diagonalization, weak and strong coupling considerations and mean-field theory. In the first example we encounter a novel deconfined quantum critical point (DQCP) with emergent O(4) symmetry. In the second example we offer a phenomenological explanation of superconducting and insulating phases of twisted bilayer graphene. Lastly, we also visit the more field-theoretic problem of boson-fermion duality in two spatial dimensions, for which we provide an exact lattice construction. This duality is closely related to the half-filled Landau level problem in quantum Hall physics.

This book offers a compact tutorial on basic concepts and tools in quantum many-body physics, and focuses on the correlation effects produced by mutual interactions. The content is divided into three parts, the first of which introduces readers to perturbation theory. It begins with the simplest examples—hydrogen and oxygen molecules—based on their effective Hamiltonians, and looks into basic properties of electrons in solids from the perspective of localized and itinerant limits. Readers will also learn about basic theoretical methods such as the linear response theory and Green functions. The second part focuses on mean-field theory for itinerant electrons, e.g. the Fermi liquid theory and superconductivity. Coulomb repulsion among electrons is addressed in the context of high-Tc superconductivity in cuprates and iron pnictides. A recent discovery concerning hydride superconductors is also briefly reviewed. In turn, the third part highlights quantum fluctuation effects beyond the mean-field picture. Discussing the dramatic renormalization effect in the Kondo physics, it provides a clear understanding of nonperturbative interaction effects. Further it introduces readers to fractionally charged quasi-particles in one and two dimensions. The last chapter addresses the dynamical mean field theory (DMFT). The book is based on the author’s long years of experience as a lecturer and researcher. It also includes reviews of recent focus topics in condensed matter physics, enabling readers to not only grasp conventional condensed matter theories but also to catch up on the latest developments in the field.

This compact but exhaustive textbook, now in its significantly revised and expanded second edition, provides an essential introduction to the field quantization of light and matter with applications to atomic physics and strongly correlated systems. Following an initial review of the origins of special relativity and quantum mechanics, individual chapters are devoted to the second quantization of the electromagnetic field and the consequences of light field quantization for the description of electromagnetic transitions. The spin of the electron is then analyzed, with particular attention to its derivation from the Dirac equation. Subsequent topics include the effects of external electric and magnetic fields on the atomic spectra and the properties of systems composed of many interacting identical particles. The book also provides a detailed explanation of the second quantization of the non-relativistic matter field, i.e., the Schrödinger field, which offers a powerful tool for the investigation of many-body problems, and of atomic quantum optics and entanglement. Finally, two new chapters introduce the finite-temperature functional integration of bosonic and fermionic fields for the study of macroscopic quantum phenomena: superfluidity and superconductivity. Several solved problems are included at the end of each chapter, helping readers put into practice all that they have learned.