How Generic Scale Invariance Influences Quantum and Classical Phase Transitions
TL;DR: In this article, the authors discuss a paradigm that has become of increasing importance in the theory of quantum phase transitions, namely, the coupling of the order-parameter fluctuations to other soft modes and the resulting impossibility of constructing a simple Landau-Ginzburg-Wilson theory in terms of order parameter only.
Abstract: This review discusses a paradigm that has become of increasing importance in the theory of quantum phase transitions, namely, the coupling of the order-parameter fluctuations to other soft modes and the resulting impossibility of constructing a simple Landau-Ginzburg-Wilson theory in terms of the order parameter only. The soft modes in question are manifestations of generic scale invariance, i.e., the appearance of long-range order in whole regions in the phase diagram. The concept of generic scale invariance and its influence on critical behavior is explained using various examples, both classical and quantum mechanical. The peculiarities of quantum phase transitions are discussed, with emphasis on the fact that they are more susceptible to the effects of generic scale invariance than their classical counterparts. Explicit examples include the quantum ferromagnetic transition in metals, with or without quenched disorder; the metal-superconductor transition at zero temperature; and the quantum antiferromagnetic transition. Analogies with classical phase transitions in liquid crystals and classical fluids are pointed out, and a unifying conceptual framework is developed for all transitions that are influenced by generic scale invariance.
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TL;DR: In this paper, the zero-temperature magnetic instabilities of two-valley semiconductors with SOI, in-plane magnetic field, and electron-electron interaction were analyzed.
Abstract: A two-dimensional electron gas (2DEG) in two-valley semiconductors has two discrete degrees of freedom given by the spin and valley quantum numbers. We analyze the zero-temperature magnetic instabilities of two-valley semiconductors with SOI, in-plane magnetic field, and electron-electron interaction. The interplay of an applied in-plane magnetic field and the SOI results in noncollinear spin quantization in different valleys. Together with the exchange intervalley interaction this results in a rich phase diagram containing four nontrivial magnetic phases. The negative nonanalytic cubic correction to the free energy, which is always present in an interacting 2DEG, is responsible for first order phase transitions. Here, we show that nonzero ground state values of the order parameters can cut this cubic nonanalyticity and drive certain magnetic phase transitions second order. We also find two tricritical points at zero temperature which together with the line of second order phase transitions constitute the quantum critical sector of the phase diagram. The predicted magnetic phases can be observed in a monolayer $\mathrm{Mo}{\mathrm{S}}_{2}$ at electron densities $n\ensuremath{\lesssim}5\ifmmode\times\else\texttimes\fi{}{10}^{12}\phantom{\rule{0.28em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}2}$.
2 citations
01 Jan 2009
TL;DR: In this article, a new heavy electron system, Yb3Pt4, where antiferromagnetic order is weakly first order in zero field, but becomes second order at a critical endpoint with the application of magnetic field, was studied.
Abstract: Heavy electron systems provide ideal venues to study a range of issues associated with quantum criticality, including unconventional electronic phases, mo- ment formation, and complex phase diagrams with exotic critical phenomena. In the heavy electron antiferromagnets studied so far, magnetic order occurs via a second order phase transition which can be tuned via pressure or field to a quantum criti- cal point. Fermi liquid behavior is found beyond the quantum critical point, and the quasiparticle mass diverges at the quantum critical point, nucleating the moments required to enable magnetic order itself. We review here our experimental results on a new heavy electron system, Yb3Pt4, where antiferromagnetic order is weakly first order in zero field, but becomes second order at a critical endpoint with the application of magnetic field. No divergence of the quasiparticle mass is observed near the quantum critical field, and instead magnetic order is driven by the exchange enhancement of the Fermi liquid itself. These data support the thesis that there are multiple routes to quantum criticality in the heavy electron compounds.
2 citations
TL;DR: In this paper, the authors review the finite temperature formulation of Eliashberg theory, both on the imaginary and real frequency axis, and briefly display some examples of the consequences of a dynamical, as opposed to static, interaction.
Abstract: Eliashberg theory is a theory of superconductivity that describes the role of phonons in providing the attractive interaction between two electrons. Phonon dynamics are taken into account, thus giving rise to retardation effects that impact the electrons, in the form of a frequency-dependent electron self-energy. In the superconducting state, this means that the order parameter, generally considered to be a static quantity in the Bardeen-Cooper-Schrieffer (BCS) theory, also becomes frequency-dependent. Here we review the finite temperature formulation of Eliashberg theory, both on the imaginary and real frequency axis, and briefly display some examples of the consequences of a dynamical, as opposed to static, interaction. Along the way we point out where further work is required, concerning the validity of some of the assumptions used.
2 citations
TL;DR: In this paper, the authors showed that the local spectral function satisfies the Fincher-Burke spin excitations of a superconducting cuprate, and that the width of incommensurate peaks in this cuprate scales to a similar finite value as at optimal doping.
Abstract: Insulating ${\mathrm{La}}_{1.95}{\mathrm{Sr}}_{0.05}{\mathrm{CuO}}_{4}$ shares with superconducting cuprates the same Fincher-Burke spin excitations, which usually are observed in itinerant antiferromagnets. The local spectral function satisfies $\ensuremath{\omega}∕T$ scaling above $\ensuremath{\sim}16\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ for this incommensurate insulating cuprate, together with previous results in commensurate insulating and incommensurate superconducting cuprates, further supporting the general prediction for square-lattice quantum spin $S=1∕2$ systems. The width of incommensurate peaks in ${\mathrm{La}}_{1.95}{\mathrm{Sr}}_{0.05}{\mathrm{CuO}}_{4}$ scales to a similar finite value as at optimal doping, strongly suggesting that they are similarly distant from a quantum critical point. They might both be limited to a finite correlation length by partial spin-glass freezing.
2 citations
TL;DR: In this paper, the scaling behavior at and near a quantum critical point separating a semimetallic from a superfluid phase was analyzed, and the renormalization group flow for a model of attractively interacting electrons with a linear dispersion around a single Dirac point.
Abstract: We analyze the scaling behavior at and near a quantum critical point separating a semimetallic from a superfluid phase. To this end we compute the renormalization group flow for a model of attractively interacting electrons with a linear dispersion around a single Dirac point. We study both ground state and finite temperature properties. In two dimensions, the electrons and the order parameter fluctuations exhibit power-law scaling with anomalous scaling dimensions. The quasi-particle weight and the Fermi velocity vanish at the quantum critical point. The order parameter correlation length turns out to be infinite everywhere in the semimetallic ground state.
2 citations
References
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Book•
01 Jan 1972
TL;DR: The field of phase transitions and critical phenomena continues to be active in research, producing a steady stream of interesting and fruitful results as discussed by the authors, and the major aim of this serial is to provide review articles that can serve as standard references for research workers in the field.
Abstract: The field of phase transitions and critical phenomena continues to be active in research, producing a steady stream of interesting and fruitful results. It has moved into a central place in condensed matter studies. Statistical physics, and more specifically, the theory of transitions between states of matter, more or less defines what we know about 'everyday' matter and its transformations. The major aim of this serial is to provide review articles that can serve as standard references for research workers in the field, and for graduate students and others wishing to obtain reliable information on important recent developments.
12,039 citations
Book•
01 Feb 1974
TL;DR: In this paper, the authors define an order parameter statistical theories of the nematic order phenomonological description of the nematic-isotopic mixtures and describe the properties of these mixtures.
Abstract: Part 1 Liquid crystals - main types and properties: introduction - what is a liquid crystal? the building blocks nematics and cholesterics smectics columnar phases more on long-, quasi-long and short-range order remarkable features of liquid crystals. Part 2 Long- and short-range order in nematics: definition of an order parameter statistical theories of the nematic order phenomonological description of the nematic-isotopic mixtures. Part 3 Static distortion in a nematic single crystal: principles of the continuum theory magnetic field effects electric field effects in an insulating nematic fluctuations in the alignment hydrostatics of nematics. Part 4 Defects and textures in nematics: observations disclination lines point disclinations walls under magnetic fields umbilics surface disclinations. Part 5 Dynamical properties of nematics: the equations of "nematodynamics" experiments measuring the Leslie co-efficients convective instabilities under electric fields molecular motions. Part 6 Cholesterics: optical properties of an ideal helix agents influencing the pitch dynamical properties textures and defects in cholesterics. Part 7 Smectics: symmetry of the main smectic phases continuum description of smectics A and C remarks on phase and precritical phenomena.
9,683 citations
TL;DR: In this paper, a general type of fluctuation-dissipation theorem is discussed to show that the physical quantities such as complex susceptibility of magnetic or electric polarization and complex conductivity for electric conduction are rigorously expressed in terms of timefluctuation of dynamical variables associated with such irreversible processes.
Abstract: A general type of fluctuation-dissipation theorem is discussed to show that the physical quantities such as complex susceptibility of magnetic or electric polarization and complex conductivity for electric conduction are rigorously expressed in terms of time-fluctuation of dynamical variables associated with such irreversible processes. This is a generalization of statistical mechanics which affords exact formulation as the basis of calculation of such irreversible quantities from atomistic theory. The general formalism of this statistical-mechanical theory is examined in detail. The response, relaxation, and correlation functions are defined in quantummechanical way and their relations are investigated. The formalism is illustrated by simple examples of magnetic and conduction problems. Certain sum rules are discussed for these examples. Finally it is pointed out that this theory may be looked as a generalization of the Einstein relation.
7,090 citations
TL;DR: In this paper, it is rigorously proved that at any nonzero temperature, a one- or two-dimensional isotropic spin-S$ Heisenberg model with finite-range exchange interaction can be neither ferromagnetic nor antiferromagnetic.
Abstract: It is rigorously proved that at any nonzero temperature, a one- or two-dimensional isotropic spin-$S$ Heisenberg model with finite-range exchange interaction can be neither ferromagnetic nor antiferromagnetic. The method of proof is capable of excluding a variety of types of ordering in one and two dimensions.
6,236 citations
30 Jun 1995
TL;DR: Weinberg as discussed by the authors presented a self-contained, up-to-date and comprehensive introduction to supersymmetry, a highly active area of theoretical physics, including supersymmetric algebras.
Abstract: In this third volume of The Quantum Theory of Fields, available for the first time in paperback, Nobel Laureate Steven Weinberg continues his masterly exposition of quantum field theory. This volume presents a self-contained, up-to-date and comprehensive introduction to supersymmetry, a highly active area of theoretical physics. The text introduces and explains a broad range of topics, including supersymmetric algebras, supersymmetric field theories, extended supersymmetry, supergraphs, non-perturbative results, theories of supersymmetry in higher dimensions, and supergravity. A thorough review is given of the phenomenological implications of supersymmetry, including theories of both gauge and gravitationally-mediated supersymmetry breaking. Also provided is an introduction to mathematical techniques, based on holomorphy and duality, that have proved so fruitful in recent developments. This book contains much material not found in other books on supersymmetry, including previously unpublished results. Exercises are included.
4,988 citations