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Quantum Phase Transition and Quantum Critical Point

Yibing Qiu

Published Oct 1, 2015• 0 citations
OpenAlex

Abstract

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

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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
Aim and Scope of this Book A plethora of systems exhibit phase transitions as the temperature or some other parameter is changed. Examples range from the ice-water phase transition observed in our daily life to the loss of ferromagnetism in iron or to the more sophisticated Mott insulator-superfluid phase transition observed in optical lattices [343]. The last five decades have witnessed a tremendous upsurge in the studies of phase transitions at finite temperature [727, 149, 333, 136, 494, 541, 556]. The success of Landau-Ginzburg theories and the concepts of spontaneous symmetry breaking and the renormalization group [27, 410, 821, 578] in explaining many of the finite temperature phase transitions occurring in nature has been spectacular. In this book, we will consider only a subclass of phase transitions called quantum phase transitions (QPTs) [154, 658, 725, 799, 185, 63, 62, 66, 141, 744] and we will discuss these mainly from the view point of recent studies of information and dynamics. QPTs are zero temperature phase transitions which are driven by quantum fluctuations and are usually associated with a non-analyticity in the ground state energy density of a quantum many-body Hamiltonian. We will focus on continuous QPTs where the order parameter vanishes continuously at the quantum critical point (QCP) at some value of the parameters which characterize the Hamiltonian. We will not discuss first order quantum phase transitions associated with an abrupt change in the order parameter. Usually, a first order phase transition is characterized by a finite discontinuity in the first derivative of the ground state energy density. A continuous QPT is similarly characterized by a finite discontinuity, or divergence, in the second derivative of the ground state energy density, assuming that the first derivative is continuous. This is of course the classical definition; we will later mention some QPTs where the ground state energy density is not necessarily singular.
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 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.
Introduction The quantum phase transitions considered so far in this book are mostly continuous, second order. They are associated with the divergence of a correlation length and of a characteristic time that renders the quantum critical point scale invariant. However, there are many important phase transitions at which the order parameter goes abruptly to zero and, more important, at which the characteristics of length and critical time do not diverge. In general there is also a latent heat , or work required, to transform one phase into another. In this and the next chapter we study these discontinuous quantum phase transitions. We proceed by considering initially some important cases of what is known as fluctuation induced quantum phase transitions to next treat a more general case of a first-order quantum phase transition. We will show through the study of these problems that the concepts of critical exponents and scaling remain useful, even though these systems do not exhibit scale invariance at their critical point. In Chapter 15 we present the scaling theory of first-order quantum phase transitions and use its results to treat some general problems. One of the most interesting cases of fluctuation-induced transitions occurs in superconductors due to the coupling of the charged carriers to the electromagnetic field. We consider initially a wider class of systems with macroscopic wave functions, the superfluids, of which superconductors are the charged version. We adopt a macroscopic approach to this problem and describe the superfluid by a complex order parameter φ , such that | φ | 2 is proportional to the density of condensed particles. The zero temperature phase diagram is expressed in terms of a control parameter, m 2 , such that, at m 2 = 0, the system presents a quantum phase transition from a superfluid state, for m 2 < 0, φ ≠ 0, to a normal state for m 2 > 0 where φ = 0. In the case of the superconductor with particles of charge q = 2 e , we will include the coupling of these particles to the electromagnetic field and study its effect in the phase diagram of these systems. We show that in the neutral superfluid, the zero temperature transition to the normal state is continuous and occurs at a quantum critical point.
Quantum phase transitions are sudden changes in the ground-state wavefunction of a many-body system that can occur as a control parameter such as a concentration or a field strength is varied. They are driven purely by the competition between quantum fluctuations and mutual interactions among constituents of the system, not by thermal fluctuations; hence they can occur even at zero temperature. Examples of quantum phase transitions in many-body physics may be found in systems ranging from high-temperature superconductors to topological insulators. A quantum phase transition usually can be characterized by nonanalyticity/discontinuity in certain order parameters or divergence of the ground state energy eigenvalue and/or its derivatives with respect to certain physical quantities. Here in a circular one-dimensional spin model with Heisenberg XY interaction and no magnetic field, we observe critical phenomena for the n0=1/N→0n_0=1/N\rightarrow0n0​=1/N→0 Mott insulator caused by a qualitative change of the boundary condition. We demonstrate in the vicinity of the transition point a sudden change in ground-state properties accompanied by an avoided level-crossing between the ground and the first excited states. Notably, our result links conventional quantum phase transitions to microscopic boundary conditions, with significant implications for quantum information, quantum control, and quantum computing.
Quantum Phase Transitions is the first book to describe in detail the fundamental changes that can occur in the macroscopic nature of matter at zero temperature due to small variations in a given external parameter. The subject plays a central role in the study of the electrical and magnetic properties of numerous important solid state materials. The author begins by developing the theory of quantum phase transitions in the simplest possible class of non-disordered, interacting systems - the quantum Ising and rotor models. Particular attention is paid to their non-zero temperature dynamic and transport properties in the vicinity of the quantum critical point. Several other quantum phase transitions of increasing complexity are then discussed and clarified. Throughout, the author interweaves experimental results with presentation of theoretical models, and well over 500 references are included. The book will be of great interest to graduate students and researchers in condensed matter physics.