Quantum Criticality and Novel Phases: A panel discussion

Physicists gathered in august at Dresden for a conference about "Quantum Criticality and Novel Phases". As one part of the meeting, nine panelists hosted an open and free-wheeling discussion on the topic of the meeting. This article outlines the discussions that took place during at this panel-meeting on the afternoon of August 3rd, 2009.Comment: Report on the panel discussion at the 2009 Dresden Meeting on Quantum Criticality and Novel Phase

A few electrons per ion scenario for the B=0 metal-insulator transition in two dimensions

We argue on the basis of experimental numbers that the B=0 metal-insulator transition in two dimensions, observed in Si-MOSFETs and in other two-dimensional systems, is likely to be due to a few strongly interacting electrons, which also interact strongly with the random positively ionized impurities. At the insulating side the electrons are all bound in pairs to the ions. On the metallic side free electrons exist which are scattered by ions dressed with electron-pairs and therefore alter the bare scattering potential of the ions. The physics at the metallic side of the transition is argued to be controlled by the classical to quantum transport cross-over leading to the observed non-monotonous dependence of the resistivity on temperature. This few electrons per ion scenario appears to be an experimentally realistic and testable scenario, which can also serve as a starting point for further theoretical analysis of the two-dimensional metal-insulator transition.Comment: 8 pages, revised version, minor change

Scaling of Entanglement close to a Quantum Phase Transitions

In this Letter we discuss the entanglement near a quantum phase transition by analyzing the properties of the concurrence for a class of exactly solvable models in one dimension. We find that entanglement can be classified in the framework of scaling theory. Further, we reveal a profound difference between classical correlations and the non-local quantum correlation, entanglement: the correlation length diverges at the phase transition, whereas entanglement in general remains short ranged.Comment: 4 pages, 4 figures, revtex. Stylistic changes and format modifie

Quantum Criticality and Novel Phases: Summary and Outlook

This conference summary and outlook provides a personal overview of the topics and themes of the August 2009 Dresden meeting on quantum criticality and novel phases. The dichotomy between the local moment and the itinerant views of magnetism is revisited and refreshed in new materials, new probes and new theoretical ideas. New universality and apparent zero temperature phases of matter move us beyond the old ideas of quantum criticality. This is accompanied by alternative pairing interactions and as yet unidentified phases developing in the vicinity of quantum critical points. In discussing novel order, the magnetic analogues of superconductivity are considered as candidate states for the hidden order that sometimes develops in the vicinity of quantum critical points in metallic systems. These analogues can be thought of as "pairing" in the particle-hole channel and are tabulated. This analogy is used to outline a framework to study the relation between ferromagnetic fluctuations and the propensity of a metal to nematic type phases which at weak coupling correspond to Pomeranchuk instabilities. This question can be related to the fundamental relations of Fermi liquid theory.Comment: Conference summary for the 2009 Dresden Meeting on Quantum Criticality and Novel Phases. 7 pages and 4 figures. The associated presentation may be found at http://www.theory.bham.ac.uk/staff/schofield/talks/Dresden

Singular Fermi Liquids

An introductory survey of the theoretical ideas and calculations and the experimental results which depart from Landau Fermi-liquids is presented. Common themes and possible routes to the singularities leading to the breakdown of Landau Fermi liquids are categorized following an elementary discussion of the theory. Soluble examples of Singular Fermi liquids (often called Non-Fermi liquids) include models of impurities in metals with special symmetries and one-dimensional interacting fermions. A review of these is followed by a discussion of Singular Fermi liquids in a wide variety of experimental situations and theoretical models. These include the effects of low-energy collective fluctuations, gauge fields due either to symmetries in the hamiltonian or possible dynamically generated symmetries, fluctuations around quantum critical points, the normal state of high temperature superconductors and the two-dimensional metallic state. For the last three systems, the principal experimental results are summarized and the outstanding theoretical issues highlighted.Comment: 170 pages; submitted to Physics Reports; a single pdf file with high quality figures is available from http://www.lorentz.leidenuniv.nl/~saarloo

Quantum phase transitions

In recent years, quantum phase transitions have attracted the interest of both theorists and experimentalists in condensed matter physics. These transitions, which are accessed at zero temperature by variation of a non-thermal control parameter, can influence the behavior of electronic systems over a wide range of the phase diagram. Quantum phase transitions occur as a result of competing ground state phases. The cuprate superconductors which can be tuned from a Mott insulating to a d-wave superconducting phase by carrier doping are a paradigmatic example. This review introduces important concepts of phase transitions and discusses the interplay of quantum and classical fluctuations near criticality. The main part of the article is devoted to bulk quantum phase transitions in condensed matter systems. Several classes of transitions will be briefly reviewed, pointing out, e.g., conceptual differences between ordering transitions in metallic and insulating systems. An interesting separate class of transitions are boundary phase transitions where only degrees of freedom of a subsystem become critical; this will be illustrated in a few examples. The article is aimed on bridging the gap between high-level theoretical presentations and research papers specialized in certain classes of materials. It will give an overview over a variety of different quantum transitions, critically discuss open theoretical questions, and frequently make contact with recent experiments in condensed matter physics.Comment: 50 pages, 7 figs; (v2) final version as publishe

Metallic behavior and related phenomena in two dimensions

For about twenty years, it has been the prevailing view that there can be no metallic state or metal-insulator transition in two dimensions in zero magnetic field. In the last several years, however, unusual behavior suggestive of such a transition has been reported in a variety of dilute two-dimensional electron and hole systems. The physics behind these observations is presently not understood. We review and discuss the main experimental findings and suggested theoretical models.Comment: To be published in Rev. Mod. Phy

How to detect fluctuating order in the high-temperature superconductors

We discuss fluctuating order in a quantum disordered phase proximate to a quantum critical point, with particular emphasis on fluctuating stripe order. Optimal strategies for extracting information concerning such local order from experiments are derived with emphasis on neutron scattering and scanning tunneling microscopy. These ideas are tested by application to two model systems - the exactly solvable one dimensional electron gas with an impurity, and a weakly-interacting 2D electron gas. We extensively review experiments on the cuprate high-temperature superconductors which can be analyzed using these strategies. We adduce evidence that stripe correlations are widespread in the cuprates. Finally, we compare and contrast the advantages of two limiting perspectives on the high-temperature superconductor: weak coupling, in which correlation effects are treated as a perturbation on an underlying metallic (although renormalized) Fermi liquid state, and strong coupling, in which the magnetism is associated with well defined localized spins, and stripes are viewed as a form of micro-phase separation. We present quantitative indicators that the latter view better accounts for the observed stripe phenomena in the cuprates.Comment: 43 pages, 11 figures, submitted to RMP; extensively revised and greatly improved text; one new figure, one new section, two new appendices and more reference