New Theoretical Approaches To Strongly Correlated Systems

For many years, the physics of strongly correlated systems was considered a theorists' playground, right at the border with pure mathematics, where physicists from the `real world' did not venture. The time has come, however, when healthy physics cannot exist without these techniques and results. Lectures on selected topics in the theory of strongly correlated systems are here presented by the leading experts in the field. Topics covered include a use of the form factor approach in low-dimensional systems, applications of quantum field theory to disorder, and dynamical mean field theory. The main divisions of the book deal with: I) Quantum Critical Points; (II) Strongly Correlated One-Dimensional Systems; (III) Strong Correlations and Disorder; and (IV) Dynamical Mean Field Theory.

This volume presents, for the very first time, an exhaustive collection of those modern numerical methods specifically tailored for the analysis of Strongly Correlated Systems. Many novel materials, with functional properties emerging from macroscopic quantum behaviors at the frontier of modern research in physics, chemistry and material science, belong to this class of systems. Any technique is presented in great detail by its own inventor or by one of the world-wide recognized main contributors. The exposition has a clear pedagogical cut and fully reports on the most relevant case study where the specific technique showed to be very successful in describing and enlightening the puzzling physics of a particular strongly correlated system. The book is intended for advanced graduate students and post-docs in the field as textbook and/or main reference, but also for other researchers in the field who appreciate consulting a single, but comprehensive, source or wishes to get acquainted, in a as painless as possible way, with the working details of a specific technique.

Focusing on the purely theoretical aspects of strongly correlated electrons, this volume brings together a variety of approaches to models of the Hubbard type - i.e., problems where both localized and delocalized elements are present in low dimensions. The chapters are arranged in three parts. The first part deals with two of the most widely used numerical methods in strongly correlated electrons, the density matrix renormalization group and the quantum Monte Carlo method. The second part covers Lagrangian, Functional Integral, Renormalization Group, Conformal, and Bosonization methods that can be applied to one-dimensional or weakly coupled chains. The third part considers functional derivatives, mean-field, self-consistent methods, slave-bosons, and extensions.

​​This is the first book that provides a detailed summary of one of the most successful new condensed matter theories - dynamical mean-field theory (DMFT) - in both static and dynamical cases of systems of different sizes. DMFT is one of the most successful approaches to describe the physical properties of systems with strong electron-electron correlations such as bulk materials, multi-layers, surfaces, 2D materials and nanostructures in both metallic and insulating phases. Strongly correlated materials usually include partially-filled localized d- or f-orbitals, and DMFT takes into account crucial for these systems time-resolved interaction between electrons when they “meet” on one atom and occupy one of these orbitals. The First Part of the book covers the general formalism of DMFT as a many-body theory, followed by generalizations of the approach on the cases of finite systems and out-of-equilibrium regime. In the last Chapter of the First Part we discuss generalizations of the approach on the case when the non-local interactions are taken into account. The Second Part of the book covers methodologies of merging DMFT with ab initio static Density Functional Theory (DFT) and Time-Dependent DFT (TDDFT) approaches. Such combined DFT+DMFT and DMFT+TDDFT computational techniques allow one to include the effects of strong electron-electron correlations at the accurate ab initio level. These tools can be applied to complex multi-atom multi-orbital systems currently not accessible to DMFT. The book helps broad audiences of students and researchers from the theoretical and computational communities of condensed matter physics, material science, and chemistry to become familiar with this state-of-art approach and to use it for reaching a deeper understanding of the properties of strongly correlated systems and for synthesis of new technologically-important materials.

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.

This book provides the first systematic discourse on a very peculiarapproach to the theory of strongly correlated systems. HubbardX-operators have been known for a long time but have not been widelyused because of their awkward algebra. The book shows that it ispossible to deal with X-operators even in the general multilevel localeigenstate system, and not just in the case of the nondegenerateHubbard model. X-operators provide the natural language for describingquasiparticles in the Hubbard subbands with unusual doping andtemperature-dependent band structures.

A comprehensive introduction to state-of-the-art quantum Monte Carlo techniques for applications in strongly-interacting systems. Including variational wave functions, stochastic samplings, the variational technique, optimisation techniques, real-time dynamics and projection methods and recent developments on the continuum space. An extensive resource for students and researchers.

Quantum many-body theory has greatly expanded its scope and depth over the past few years, treating more deeply long-standing issues like phase transitions and strongly-correlated systems, and simultaneously expanding into new areas such as cold atom physics and quantum information. This collection of contributions highlights recent advances in all these areas by leaders in their respective fields. Also included are some historic perspectives by L P Gor'kov and S T Belyaev, Feenberg Medal Recipients at this conference, and Nobel Laureate P W Anderson gives his unique outlook on the future of physics. The volume covers the key topics in many-body theory, tied together through advances in theoretical tools and computational techniques, and a unifying theme of fundamental approaches to quantum many-body physics. Contents: Feenberg Medal Session: Surface and Superconductivity (L P Gor'kov); The Future Lies Ahead (P W Anderson); Strongly Correlated Systems and Phase Transitions: Quantum Matters: Physics Beyond Landau's Paradigms (T Senthil); Recent Applications of the DMRG Method (K Hallberg); Quantum Fluids and Solids: Monolayer Charged Quantum Films: A Quantum Simulation Study (K Wierschem & E Manousakis); Analysis of the Interatomic Potential of the Helium Systems (S Ujevic & S A Vitiello); Nuclear Physics and QCD: Quantum Phase Transitions in Mesoscopic Systems (F Iachello); New Approaches to Strong Coupling Lattice QCD (S Chandrasekharan); Cold Atoms and Quantum Information: Superfluid Regimes in Degenerate Atomic Fermi Gases (G V Shlyapnikov); Bosons in Optical Lattices (S L Rolston); Complex Systems: Spin Textures and Random Fields in Dirty Quantum Hall Ferromagnets (J T Chalker); Dissipative Quantum Disordered Models (L F Cugliandolo); and other papers. Readership: Theoretical physicists in condensed matter, nuclear physics and QCD, atomic physics and quantum information.