In the previous chapter, we discussed both the insulator–superconductor and the insulator–metal transitions. As such transitions are disorder or magnetic-field tuned, thermal fluctuations play no role. Phase transitions of the insulator–superconductor or insulator–metal type are called quantum phase transitions. Such phase transitions are not controlled by changing the temperature, as in the melting of ice or the λ-point of liquid helium, but rather by changing some system parameter, such as the number of defects or the concentration of charge carriers. In all such instances, the tuning parameter transforms the system between quantum mechanical states that either look different topologically (as in the transition between localized and extended electronic states) or have distinctly different magnetic properties. As quantum mechanics underlies such phase transitions, all quantum phase transitions obtain at the absolute zero of temperature and thus are governed by a T = 0 quantum critical point. While initially surprising, this state of affairs is expected, because quantum mechanics is explicitly a zero-temperature theory of matter. Of course, this is of no surprise to chemists who have known for quite some time that numerous materials can exhibit vastly distinct properties simply by changing the chemical composition and, most importantly, that such transformations persist down to zero temperature. Common examples include turning insulators such as the layered cuprates into superconductors simply by chemical doping or semiconductors into metals once again by doping, or ferromagnets such as Li(Ho, Tb) x Y 1- x F 4 into a spin glass (AR1998) by altering x .
In the previous chapter, we discussed both the insulator–superconductor and the insulator–metal transitions. As such transitions are disorder or magnetic-field tuned, thermal fluctuations play no role. Phase transitions of the insulator–superconductor or insulator–metal type are called quantum phase transitions. Such phase transitions are not controlled by changing the temperature, as in the melting of ice or the λ-point of liquid helium, but rather by changing some system parameter, such as the number of defects or the concentration of charge carriers. In all such instances, the tuning parameter transforms the system between quantum mechanical states that either look different topologically (as in the transition between localized and extended electronic states) or have distinctly different magnetic properties. As quantum mechanics underlies such phase transitions, all quantum phase transitions obtain at the absolute zero of temperature and thus are governed by a T = 0 quantum critical point. While initially surprising, this state of affairs is expected, because quantum mechanics is explicitly a zero-temperature theory of matter. Of course, this is of no surprise to chemists who have known for quite some time that numerous materials can exhibit vastly distinct properties simply by changing the chemical composition and, most importantly, that such transformations persist down to zero temperature. Common examples include turning insulators such as the layered cuprates into superconductors simply by chemical doping or semiconductors into metals once again by doping, or ferromagnets such as Li(Ho, Tb) x Y 1- x F 4 into a spin glass (AR1998) by altering x .
Zero-temperature or quantum phase transitions in itinerant electronic systems both with and without quenched disordered are discussed. Phase transitions considered include, the ferromagnetic transition, the antiferromagnetic transition, the superconductor-metal transition, and various metal-insulator transitions. Emphasis is placed on how to determine the universal properties that characterize these quantum phase transitions. For the first three of the phase transitions listed above, one of the main physical ideas established is that in zero-temperature systems there are soft or slow modes that exist in addition to the soft order parameter fluctuations, and that these modes can couple to the critical modes. These extra soft modes are shown to have a profound effect on the quantum critical properties. For quantum phase transitions involving zero wavenumber order parameters, i.e., the ferromagnetic and superconductor-metal transitions, these extra modes effectively lead to long-ranged effective interactions between order parameter fluctuations, which in turn lead to exactly soluble critical behaviors. For the antiferromagnetic case, we argue that while in low enough dimensions disorder fluctuation effects tend to destroy long-range order, quantum fluctuations counteract this effect and in some parameter regions manage to re-establish antiferromagnetic long-range order. For the metal-insulator transition, some recent new ideas are reviewed. In particular, it is pointed out that for interacting disordered electrons, one expects that in high dimensions the metal-insulator transition is related to the phase transition that occurs in random-field magnets in high dimensions. If the analogy also holds in three dimensions this suggests that the metal-insulator transition might have glassy characteristics.
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 behaviour 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 is 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 at bridging the gap between high-level theoretical presentations and research papers specialized in certain classes of materials. It will give an overview on a variety of different quantum transitions, critically discuss open theoretical questions, and frequently make contact with recent experiments in condensed matter physics.
Superconductor-insulator transitions, especially in thin films, can provide the simplest examples of the continuous quantum phase transition paradigm. Quantum phase transitions differ from thermal phase transitions in that they occur at zero temperature when the ground state of a system is changed in response to a variation of an external parameter of the Hamiltonian. In the example of the superconductor-insulator transition, this control parameter could be the parallel or perpendicular magnetic field, disorder, or charge density. Quantum phase transitions are studied through measurements at nonzero temperature of physical behaviors influenced by the quantum fluctuations associated with the transition. This review will focus on experimental aspects of superconductor-insulator transition in disordered films that are effectively two-dimensional. In particular, the evidence for quantum critical behavior in the various types of transitions will be presented. The various theoretical scenarios for the transitions will also be discussed along with the extent to which they are supported by experiment. Open questions relating to the nature of the very puzzling insulating regime and whether there are many different types of superconductor-insulator transitions will be presented. Although this research area is more than 20 years old, rather central issues are not resolved.
At a quantum critical point the ground state of a many-particle quantum system undergoes a phase transition when some control parameters such as pressure, magnetic field, or chemical composition is varied. The universal behaviour characteristic for such quantum phase transitions often affects a wide temperature range and gives rise to novel material properties. This chapter gives a short overview over five lectures held during the Les Houches summer school ‘Quantum theory from small to large scales’ in 2010. After an introductory chapter, field driven magnetic quantum phase transitions of insulators are used as an example to discuss some of the concepts underlying quantum phase transitions. Both experimentally and theoretically, quantum phase transitions in metals are much less understood compared to insulating systems. After a brief review of the standard approach to describe those systems, the importance of multiple time scales and associated multiple critical exponents z are discussed. Finally, emergent gauge theories close to critical points are investigated. As an example, it discusses why a gauge theory describes the (classical) phase transitions of a nematic, if topological defects are suppressed.
The past decade has seen a substantial rejuvenation of interest in the study of quantum phase transitions, driven by experiments on cuprate superconductors, heavy fermion materials, organic conductors, and related compounds. Although quantum phase transitions in simple spin systems, like the Ising model in a transverse field, were studied in the early 1970s, much of the subsequent theoretical work examined a particular example: the metal–insulator transition. While this is a subject of considerable experimental importance, the greatest theoretical progress was made for the case of the Anderson transition of non-interacting electrons, which is driven by localization of the electronic states in the presence of a random potential. The critical properties of this transition of noninteracting electrons constituted the primary basis upon which most condensed matter physicists have formed their intuition on the behavior of the systems near a quantum phase transition. However, it is clear that strong electronic interactions play a crucial role in the systems of current interest noted earlier, and simple paradigms for the behavior of such systems near quantum critical points are not widely known. It is the purpose of this book to move interactions to center stage by describing and classifying the physical properties of the simplest interacting systems undergoing a quantum phase transition. The effects of disorder will be neglected for the most part but will be considered in the concluding chapters. Our focus will be on the dynamical properties of such systems at nonzero temperature, and it will become apparent that these differ substantially from the noninteracting case.
Discussing quantum phase transition and quantum critical point Main Viewpoints and Conclusions: In physics, a quantum phase transition (QPT) is a phase transition between different quantum phases (phases of matter at zero temperature). Contrary to classical phase transitions, quantum phase transitions can only be accessed by varying a physical parameter—such as magnetic field or pressure—at absolute zero temperature. The transition describes an abrupt change in the ground state of a many-body system due to its quantum fluctuations.[1] In fact and details, the study of the quantum phase transition and quantum critical point, is the study about of a material in a condition which with a definite electromagnetic and pressure environment, and when the temperature continues change to lower, until reaches absolute zero temperature, the properties changing of this material with the changes of the environment temperature (whether it is a single kind of atom or more kinds of atoms of the crystal compound, and especially with regards to solid material). With a definite electromagnetic and pressure environment, the environment temperature continues change to lower, until reaches absolute zero temperature, in the process, the material lost its energy continuously, so, the energy both of the all extranuclear charges and all nucleuses (main is π-mesons body) of the material also is go into further lower continuously. Meanwhile, the volume density, natural frequency and energy level of the extranuclear charges go into further lower continuously; the difference of the volume charge density, natural frequency and energy level between all parts of the material becomes to smaller, and reaches the same and consistency at absolute zero temperature. In the state, all atoms of the material at the same and lowest energy level of their ground state, the extranuclear-charges of all atoms with the same density and polymerized into a single complete whole and agglomerate together with all nucleuses, namely, the material is being its Bose-Einstein condensate (BEC).[2][3][4][5] The process of the volume density, natural frequency and energy level of the extranuclear charges go into further lower continuously; the difference of the volume charge density, natural frequency and energy level between all parts of the material becomes smaller, also is a process that the energy levels of every parts of the extranuclear charges goes into more lower state which higher than the lowest energy level-ground state, and this is the weak first-order quantum phase transition which we called that the energy levels from higher to lower but still higher than the lowest energy level-ground state yet; further, we called the quantum state transition is second-order quantum phase transition which the energy levels of every parts of the extranuclear charges from many different higher energy levels goes into the same and lowest energy level-ground state after the material reaches into and at its Bose-Einstein condensate; and the environment condition (combined effect generated by magnetic-field, pressure and temperature) that is the quantum phase dividing line or called quantum critical point which makes the material reaches into its Bose-Einstein condensate and the all extranuclear charges from the state with many different volume charge densities, natural frequencies and energy levels transform into a single complete whole body which with the same and unique volume charge density, natural frequency and energy level at its ground state; or, in other words, the quantum critical point is the dividing line of the two state that the all extranuclear charges with many different volume charge densities, natural frequencies and energy levels or the all extranuclear charges with the same and unique volume charge density, natural frequency and energy level at its ground state. Contrary to the case of a material into its Bose-Einstein condensate, after temperature rise and beyond the quantum critical point, the material would deviate from its Bose-Einstein condensate, the extranuclear charge-body separates from the all nucleuses, and the all nucleuses returns to their free states. Same time, the volume density of every parts of the extranuclear charge-body whether combined into atomic bonds or not, all changes into and at non same and unique state, the energy levels of the extranuclear charge-body appear as separate and in a discrete state, and then restoration and presentation quantum behaviors in the microscopic scale of the material. References & Related stories [1] Quantum phase transition https://en.wikipedia.org/wiki/Quantum_phase_transition [2] Bose-Einstein condensate https://en.wikipedia.org/wiki/Bose%E2%80%93Einstein_condensate [3] A New Model of Atomic Structure http://vixra.org/abs/1401.0147 [4] The Causes and Mechanism of Atomic Energy Levels quantum http://vixra.org/abs/1402.0104 [5] The Structure, State and Properties of Matter in Bose-Einstein Condensate http://vixra.org/abs/1509.0184 [6] Critical behavior at a dynamic vortex insulator-to-metal transition Science, 2015; 349 (6253): 1202 Doi: 10.1126/science.1260507 [7] Inhomogeneity of charge-density-wave order and quenched disorder in a high-Tc superconductor Nature, 525, 359–362 (17 September 2015) Doi: 10.1038/nature14987 [8] The mechanism of charge density wave in Pt-based layered superconductors: SrPt2As2 and LaPt2Si2 Nature, scientific Reports 5, 15052(2015) Doi: 10.1038/srep15052 YuQuan Road, Zhao Feng Yuan Section, 3rd block, Feng Tai District, Beijing, CHINA