arXiv subjects
Publications and source records attributed to D. Belitz.
Dephasing of electrons due to the electron-electron interaction has recently been the subject of a controversial debate, with different calculations yielding mutually incompatible results. In this paper we prove, by means of Ward identities, that neither a Coulomb interaction nor a short-ranged model interaction can lead to phase breaking at zero temperature in spatial dimensions d>2.
The problem of noninteracting electrons in the presence of annealed magnetic disorder, in addition to nonmagnetic quenched disorder, is considered. It is shown that the proper physical interpretation of this model is one of electrons interacting via a potential that is long-ranged in time, and that its technical analysis by means of renormalization group techniques must also be done in analogy to the interacting problem. As a result, and contrary to previous claims, the model does not simply describe a metal-insulator transition in $d=2+ε$ ($ε\ll 1$) dimensions. Rather, it describes a transition to a ferromagnetic state that, as a function of the disorder, precedes the metal-insulator transition close to $d=2$. In $d=3$, a transition from a paramagnetic metal to a paramagnetic insulator is possible.
A comprehensive theory of the quantum phase transition in clean, itinerant Heisenberg ferromagnets is presented. It is shown that the standard mean-field description of the transition is invalid in spatial dimensions $d\leq 3$ due to the existence of soft particle-hole excitations that couple to the order parameter fluctuations and lead to an upper critical dimension $d_c^+ = 3$. A generalized mean-field theory that takes these additional modes into account predicts a fluctuation-induced first-order transition. In a certain parameter regime, this first-order transition in turn is unstable with respect to a fluctuation-induced second-order transition. The quantum ferromagnetic transition may thus be either of first or of second-order, in agreement with experimental observations. A detailed discussion is given of the stability of the first-order transition, and of the critical behavior at the fluctuation-induced second-order transition. In $d=3$, the latter is mean field-like with logarithmic corrections to scaling, and in $d<3$ it can be controlled by means of a $3-ε$ expansion.
A comprehensive theory is developed that describes the coexistence of p-wave, spin-triplet superconductivity and itinerant ferromagnetism. It is shown how to use field-theoretic techniques to derive both conventional strong-coupling theory, and analogous gap equations for superconductivity induced by magnetic fluctuations. It is then shown and discussed in detail that the magnetic fluctuations are generically stronger on the ferromagnetic side of the magnetic phase boundary, which substantially enhances the superconducting critical temperature in the ferromagnetic phase over that in the paramagnetic one. The resulting phase diagram is compared with the experimental observations in UGe_2 and ZrZn_2.
The quantum phase transition in clean itinerant ferromagnets is analyzed. It is shown that soft particle-hole modes invalidate Hertz's mean-field theory for $d \leq 3$. A renormalized mean-field theory predicts a fluctuation-induced first order transition for $1 < d \leq 3$, whose stability is analyzed by renormalization group techniques. Depending on microscopic parameter values, the first order transition can be stable, or be pre-empted by a fluctuation-induced second order transition. The critical behavior at the latter is determined. The results are in agreement with recent experiments.
General conditions are formulated that allow to determine which quantum phase transitions in itinerant electron systems can be described by a local Landau-Ginzburg-Wilson or LGW theory solely in terms of the order parameter. A crucial question is the degree to which the order parameter fluctuations couple to other soft modes. Three general classes of zero-wavenumber order parameters, in the particle-hole spin-singlet and spin-triplet channels, and in the particle-particle channel, respectively, are considered. It is shown that the particle-hole spin-singlet class does allow for a local LGW theory, while the other two classes do not. The implications of this result for the critical behavior at various quantum phase transitions are discussed, as is the connection with nonanalyticities in the wavenumber dependence of order parameter susceptibilities in the disordered phase.
Two predictions are made for properties of the ferromagnetic superconductors discovered recently. The first one is that spin-triplet, p-wave pairing in such materials will give the magnons a mass inversely proportional to the square of the magnetization. The second one is based on a specific mechanism for p-wave pairing, and predicts that the observed broad anomaly in the specific heat of URhGe will be resolved into a split transition with increasing sample quality. These predictions will help discriminate between different possible mechanisms for ferromagnetic superconductivity.
It is shown that the critical temperature for spin-triplet, p-wave superconductivity mediated by spin fluctuations is generically much higher in a Heisenberg ferromagnetic phase than in a paramagnetic one, due to the coupling of the magnons to the longitudinal magnetic susceptibility. Together with the tendency of the low-temperature ferromagnetic transition in very clean Heisenberg magnets to be of first order, this qualitatively explains the phase diagram recently observed in UGe_2.
Many-body interactions in effective field theories for disordered interacting electrons are considered. It is shown that three-body and higher interaction terms are generated in perturbation theory, and some of the physical consequences of these interactions are discussed. It is shown in particular that they will in general be important for any effects governed by strong-coupling fixed points. This implies that the usual generalized nonlinear sigma-model for disordered electron systems is incomplete, and not suitable for studying strong-coupling effects.
An effective field theory is derived that describes the quantum critical behavior of itinerant ferromagnets as the transition is approached from the ferromagnetic phase. This complements a recent study of the critical behavior on the paramagnetic side of the phase transition, and investigates the role of the ferromagnetic Goldstone modes near criticality. We find that the Goldstone modes have no direct impact on the critical behavior, and that the critical exponents are the same as determined by combining results from the paramagnetic phase with scaling arguments.
An overview is given of the long-time and long-distance behavior of correlation functions in both classical and quantum statistical mechanics. After a simple derivation of the classical long-time tails in equilibrium time correlation functions, we discuss analogous long-distance phenomena in nonequilibrium classical systems. The paper then draws analogies between these phenomena and similar effects in quantum statistical mechanics, with emphasis on the soft modes that underly long-time tails and related phenomena. We also elucidate the interplay between critical phenomena and long-time tails, using the classical liquid-gas critical point and the quantum ferromagnetic transition as examples.
It is argued that the phase transition in low-T_c clean itinerant ferromagnets is generically of first order, due to correlation effects that lead to a nonanalytic term in the free energy. A tricritical point separates the line of first order transitions from Heisenberg critical behavior at higher temperatures. Sufficiently strong quenched disorder suppresses the first order transition via the appearance of a critical endpoint. A semi-quantitative discussion is given in terms of recent experiments on MnSi and UGe_2. It is then shown that the critical temperature for spin-triplet, p-wave superconductivity mediated by spin fluctuations is generically much higher in a Heisenberg ferromagnetic phase than in a paramagnetic one, due to the coupling of magnons to the longitudinal magnetic susceptibility. This qualitatively explains the phase diagram recently observed in UGe_2 and ZrZn_2.
An effective field theory is derived that describes the quantum critical behavior of itinerant ferromagnets in the presence of quenched disorder. In contrast to previous approaches, all soft modes are kept explicitly. The resulting effective theory is local and allows for an explicit perturbative treatment. It is shown that previous suggestions for the critical fixed point and the critical behavior are recovered under certain assumptions. The validity of these assumptions is discussed in the light of the existence of two different time scales. It is shown that, in contrast to previous suggestions, the correct fixed point action is not Gaussian, and that the previously proposed critical behavior was correct only up to logarithmic corrections. The connection with other theories of disordered interacting electrons, and in particular with the resolution of the runaway flow problem encountered in these theories, is also discussed.
The quantum critical behavior of disordered itinerant ferromagnets is determined exactly by solving a recently developed effective field theory. It is shown that there are logarithmic corrections to a previous calculation of the critical behavior, and that the exact critical behavior coincides with that found earlier for a phase transition of undetermined nature in disordered interacting electron systems. This confirms a previous suggestion that the unspecified transition should be identified with the ferromagnetic transition. The behavior of the conductivity, the tunneling density of states, and the phase and quasiparticle relaxation rates across the ferromagnetic transition is also calculated.
The conductivity and the tunneling density of states of disordered itinerant electrons in the vicinity of a ferromagnetic transition at low temperature are discussed. Critical fluctuations lead to nonanalytic frequency and temperature dependences that are distinct from the usual long-time tail effects in a disordered Fermi liquid. The crossover between these two types of behavior is proposed as an experimental check of recent theories of the quantum ferromagnetic critical behavior. In addition, the quasiparticle properties at criticality are shown to be those of a marginal Fermi liquid.
The behavior of the conductivity and the density of states, as well as the phase relaxation time, of disordered itinerant electrons across a quantum ferromagnetic transition is discussed. It is shown that critical fluctuations lead to anomalies in the temperature and energy dependence of the conductivity and the tunneling density of states, respectively, that are stronger than the usual weak-localization anomalies in a disordered Fermi liquid. This can be used as an experimental probe of the quantum critical behavior. The energy dependence of the phase relaxation time at criticality is shown to be that of a marginal Fermi liquid.
This paper discusses why the usual notion that quantum phase transitions can be mapped onto classical phase transitions in a higher dimension, and that this makes the former uninteresting from a fundamental theoretical point of view, is in general misleading. It is shown that quantum phase transitions are often qualitatively different from their classical counterparts due to (1) long-ranged effective interactions that are induced by soft modes, and (2) in the presence of quenched disorder, an extreme anisotropy of space-time. These points are illustrated using various magnetic phase transitions as examples.
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.