Exotic Phases and Quantum Phase Transitions: Model Systems and Experiments (S Sachdev) Experimentally Realized Correlated Electron Materials: From Superconductors to Topological Insulators (C Kallin) The Quantum Hall Effect - An Overview (A Stern) One Dimensional Quantum Condensed Matter (I Affleck) Strongly Correlated Quantum Systems with Ultracold Atoms in Optical Lattices (I Bloch) Numerical Methods Using Matrix and Tensor Product Wave Functions (S R White)
Exotic Phases and Quantum Phase Transitions: Model Systems and Experiments (S Sachdev) Experimentally Realized Correlated Electron Materials: From Superconductors to Topological Insulators (C Kallin) The Quantum Hall Effect - An Overview (A Stern) One Dimensional Quantum Condensed Matter (I Affleck) Strongly Correlated Quantum Systems with Ultracold Atoms in Optical Lattices (I Bloch) Numerical Methods Using Matrix and Tensor Product Wave Functions (S R White)
Exotic phases of matter represent a paradigm shift in condensed matter physics, transcending classical thermodynamic states and embracing quantum mechanical principles. These phases, including topological insulators, quantum spin liquids, and time crystals, exhibit emergent properties driven by symmetry breaking, entanglement, and quantum coherence. This paper explores the fundamental principles governing these novel phases, recent breakthroughs in their realization, and their implications for quantum computing and materials science. Emphasis is placed on theoretical models such as the Kitaev honeycomb lattice and experimental advances in ultracold atom traps and strongly correlated electron systems. By reviewing current challenges and prospects, this study outlines a roadmap for navigating this new frontier in physics.
The Enigma of the Pseudogap Phase of the Cuprate Superconductors (Debanjan Chowdhury and Subir Sachdev) Resonant Spin Excitations in Unconventional Heavy Fermion Superconductors and Kondo Lattice Comppounds (Peter Thalmeier and Alireza Akbari) Quantum Critical Heavy Fermion Metal Ybrh2si2 (Gertrud Zwicknagl) Universality and Convergence of Energy Scales at Quantum Critical Points in Local and Lattice Models (A C Hewson, D J G Crow and Y Nishikawa) Unparticles in Strongly Correlated Electron Matter (Philip W Phillips) Fidelity Approach to Quantum Phase Transitions in Quantum Ising Model (Bogdan Damski) Dynamics of Quantum Phase Transitions: Quantum Kibble-Zurek Mechanism (Jacek Dziarmaga) Theory of Temporal Fluctuations in Isolated Quantum Systems (L Campos Venuti)
Presenting the physics of the most challenging problems in condensed matter using the conceptual framework of quantum field theory, this book is of great interest to physicists in condensed matter and high energy and string theorists, as well as mathematicians. Revised and updated, this second edition features new chapters on the renormalization group, the Luttinger liquid, gauge theory, topological fluids, topological insulators and quantum entanglement. The book begins with the basic concepts and tools, developing them gradually to bring readers to the issues currently faced at the frontiers of research, such as topological phases of matter, quantum and classical critical phenomena, quantum Hall effects and superconductors. Other topics covered include one-dimensional strongly correlated systems, quantum ordered and disordered phases, topological structures in condensed matter and in field theory and fractional statistics.
We review recent experimental and theoretical progress in realizing and simulating many-body phases of ultracold atoms in optical lattices, which gives access to analog quantum simulations of fundamental model Hamiltonians for strongly correlated condensed matter systems, such as the Hubbard model. After a general introduction to quantum gases in optical lattices, their preparation and cooling, and measurement techniques for relevant observables, we focus on several examples, where quantum simulations of this type have been performed successfully during the past years: Mott-insulator states, itinerant quantum magnetism, disorder-induced localization and its interplay with interactions, and topological quantum states in synthetic gauge fields.
Open questions related with heavy electrons, H.R. Ott electron spectroscopy of strongly correlated systems, J.W. Allen single hole in 1D and 2D hubbard model, S. Sorella surface acoustic wave studies of the FQHE, R.L. Willett Chern-Simons-Landau-Ginzburg theory of the FQHE and its experimental prediction, S.C. Zhang magnetic fluctuations in La2-xSrxCuO4, G. Aeppli single particle spectral function for the large U Hubbard model, P. Wolfe strongly correlated systems in infinite dimensions and their zero-dimensional counterpart, G. Kotliar stable hc-e vortices in a gauge theory of superconductivity in strongly correlated systems, S. Sachdev electronic mechanisms for superconductivity in doped C60, G. Baskaran weakly correlated electrons - many questions and few answers, H.J. Schulz normal state properties of the high Tc oxides - gauge theories, L. Loffe single particle and optical gaps in charge-transfer insulators, Y. Bang et al a renormalization group approach for many-Fermion problems, R. Shankar spin singlet quantum hall effect and nonabelian Landau-Ginzburg theory, A. Balatsky De Haas-Van Alphen and Shubnikov-De Haas oscillations in strongly correlated electron gas, P. Lederer et al strongly correlated Fermi liquid and the normal state of high Tc superconductors, Z. Wang determinant Monte Carlo for the Hubbard model with arbitrarily gauged auxiliary fields, A.M. Tremblay spin-charged coupling in doped Mott insulators, J. Wheatley.
A quantum simulator is a well-controlled quantum system which can be used to simulate another quantum system. Quantum degenerate gases confined by optical standing waves(optical lattices) have been considered to simulate condensed matter systems. We focus on two issues in this problem. The first one is the realization of interesting quantum phases by engineering Hamiltonians with the cold atoms toolbox. Secondly, the systems we studied are often intractable to analytical methods, which makes it a crucial issue to solve them with numerical methods. For the first issue we find several interesting phases can be studied with cold atoms in optical lattices. We show that a p-wave superfluid is stablized through a dissipation blockade mechanism. This mechanism also induces a new insulator formed by p-wave Feshbach molecules. We find that the anisotropic nature of interaction between polar molecules or dipolar atoms can be used to realize two charge density waves with different patterns and a supersolid phase which has not been found conclusively in the condensed matter system. Finally, we propose to realize a long sought spin liquid phase with hard-core bosons subject to a spin-dependent lattice and Raman induced hoppings. For the second issue we choose to numerically study these systems with the so-called tensor network algorithm which is a variational method based on the matrix(tensor) product states product states which are designed to approximate generic wave functions from their entanglement properties. In general the tensor network algorithm has advantages that it is applicable beyond one dimension, and can be used to study physical properties in the thermodynamic limit directly. We apply this method to map out the phase diagrams of the above systems. Furthermore, we show that it is capable of capturing the phase diagram of a frustrated magnetism model, the Heisenberg model on a checkerboard lattice. The great controllability and isolation from the environment of a cold atom system offer a playground to study interesting physics in strongly correlated systems. Several proposed control schemes in this thesis have been demonstrated in experiments. By providing detailed evidence from numerical simulations, this work addresses practical routes to novel quantum phases.