Open Access
Quantum Scaling in Many-Body Systems
Reads0
Chats0
TLDR
In this article, a scaling theory of the Mott transition was introduced to study the quantum nature of the many-body instability in strongly correlated electronic materials, which can be generally associated with the setting of Fermi-liquid behavior with decreasing temperature in 3D strongly interacting electronic systems.Abstract:
The theory of quantum critical phenomena is introduced to study some current many-body problems in condensed matter physics. Renormalization group concepts are applied to strongly correlated electronic materials which are close to a zero-temperature instability. These systems have enhanced effective masses and susceptibility. Scaling arguments yield the exponents which govern the critical behavior of these quantities in terms of the usual critical exponents associated with a zero-temperature phase transition. We show the existence of a new energy scale, related to the quantum nature of the many-body instability, which can be generally associated with the setting of Fermi-liquid behavior with decreasing temperature in three-dimensional strongly interacting electronic systems. The theory of quantum critical phenomena is used to investigate the Kondo lattice problem, which provides a model to describe heavy-fermion systems and to introduce a scaling theory of the Mott transition with special emphasis on charge fluctuation effects. However, this report is not a review on heavy fermions and Mott insulators. The microscopic theories of these systems are still controversial and present some of the most challenging and instigating problems in condensed matter physics. This state of affairs stimulated the author to review and extend the scaling approach. The scaling theory we develop provides a powerful tool, based on the notion of universality, to understand the physical properties of correlated systems beyond the mean-field level. This is illustrated by our treatment of the one-dimensional Hubbard model, where, although the Fermi-liquid fixed point does not survive the fluctuations, the scaling approach is still useful. Finally, we discuss briefly how disorder affect our results.read more
Citations
More filters
Journal ArticleDOI
The break-up of heavy electrons at a quantum critical point
J. Custers,Philipp Gegenwart,Heribert Wilhelm,K. Neumaier,Yoshifumi Tokiwa,O. Trovarelli,C. Geibel,Frank Steglich,Catherine Pépin,Piers Coleman +9 more
TL;DR: It is inferred that all ballistic motion of electrons vanishes at a QCP, forming a new class of conductor in which individual electrons decay into collective current-carrying motions of the electron fluid.
Journal ArticleDOI
Classical correlation and quantum discord in critical systems
TL;DR: In this article, the behavior of quantum and classical pairwise correlations in critical systems, with the quantumness of the correlations measured by the quantum discord, is analyzed for general real density matrices displaying ${Z}_{2}$ symmetry.
Journal ArticleDOI
Fidelity approach to quantum phase transitions
TL;DR: In this article, the authors review the quantum fidelity approach to quantum phase transitions in a pedagogical manner and relate all established but scattered results on the leading term of the fidelity into a systematic theoretical framework, which might provide an alternative paradigm for understanding quantum critical phenomena.
Journal ArticleDOI
Singular or Non-Fermi Liquids
TL;DR: An introductory survey of the theoretical ideas and calculations and experimental results which depart from Landau Fermi liquids is presented in this paper, where the common themes and possible routes to the singularities leading to breakdown of Landau fermi liquid are categorized.
Book
Critical Dynamics: A Field Theory Approach to Equilibrium and Non-Equilibrium Scaling Behavior
TL;DR: In this article, near-equilibrium critical dynamics: 1. Equilibrium critical phenomena 2. Stochastic dynamics 3. Dynamic scaling 4. Dynamic perturbation theory 5. Dynamic renormalization group 6. Hydrodynamic modes and reversible mode couplings 7. Scale invariance in Non-Equilibrium Systems 8. Nonequilibrium Critical dynamics 9. Reaction-diffusion systems 10. Active to absorbing state transitions 11. Driven diffusive systems and growing interfaces Index
References
More filters
Journal ArticleDOI
Disordered electronic systems
TL;DR: In this article, a review of the progress made in the last several years in understanding the properties of disordered electronic systems is presented, focusing on the metal-to-insulator transition and problems associated with the insulator.
Journal ArticleDOI
Boson localization and the superfluid-insulator transition.
TL;DR: It is argued that the superfluid-insulator transition in the presence of disorder may have an upper critical dimension dc which is infinite, but a perturbative renormalization-group calculation wherein the critical exponents have mean-field values for weak disorder above d=4 is also discussed.
Journal ArticleDOI
Absence of Mott Transition in an Exact Solution of the Short-Range, One-Band Model in One Dimension
Elliott H. Lieb,F. Y. Wu +1 more
TL;DR: In this paper, the short-range, one-band model for electron correlations in a narrow energy band is solved exactly in the one-dimensional case, and the ground-state energy, wave function, and chemical potentials are obtained, and it is found that the ground state exhibits no conductor-insulator transition as the correlation strength is increased.
Book
Metal-insulator transitions
TL;DR: In this article, a discussion is given of some aspects of the metal insulator transition and the status of the "minimum metallic conductivity" is discussed, and the concept is valid for liquids and in some, but not all, solid systems.
Journal ArticleDOI
Quantum critical phenomena
TL;DR: In this paper, the authors proposed an approach to the study of critical phenomena in quantum-mechanical systems at zero or low temperatures, where classical free-energy functionals of the Landau-Ginzburg-Wilson sort are not valid.