Fermion Self-energy Research Articles

Quantum Critical Behavior Near a Density-Wave Instability in an Isotropic Fermi Liquid

We study the quantum critical behavior in an isotropic Fermi liquid in the vicinity of a zero-temperature density-wave transition at a finite wave vector qc. We show that, near the transition, the Landau damping of the soft bosonic mode yields a crossover in the fermionic self-energy from Sigma(k,omega) approximately Sigma(k) to Sigma(k,omega) approximately Sigma(omega), where k and omega are momentum and frequency. Because of this self-generated locality, the fermionic effective mass diverges right at the quantum critical point, not before; i.e., the Fermi liquid survives up to the critical point.

Non-Fermi-liquid specific heat of normal degenerate quark matter

We compute the low-temperature behavior of the specific heat of normal (non-color-superconducting) degenerate quark matter as well as that of an ultradegenerate electron gas. Long-range magnetic interactions lead to non-Fermi-liquid behavior with an anomalous leading $T\mathrm{ln}{T}^{\ensuremath{-}1}$ term. Depending on the thermodynamic potential used as a starting point, this effect appears as a consequence of the logarithmic singularity in the fermion self-energy at the Fermi surface or directly as a contribution from the only weakly screened quasistatic magnetic gauge bosons. We show that a calculation of Boyanovsky and de Vega claiming the absence of a leading $T\mathrm{ln}{T}^{\ensuremath{-}1}$ term missed it by omitting vector boson contributions to the internal energy. Using a formulation which collects all nonanalytic contributions in bosonic ring diagrams, we systematically calculate corrections beyond the well-known leading-log approximation. The higher-order terms of the low-temperature expansion turn out to also involve fractional powers ${T}^{(3+2n)/3}$ and we explicitly determine their coefficients up to and including order ${T}^{7/3}$ as well as the subsequent logarithmically enhanced term ${T}^{3}\mathrm{ln}(c/T)$. We derive also a hard-dense-loop resummed expression which contains the infinite series of anomalous terms to leading order in the coupling and which we evaluate numerically. At low temperatures, the resulting deviation of the specific heat from its value in naive perturbation theory is significant in the case of strongly coupled normal quark matter and thus of potential relevance for the cooling rates of (proto)neutron stars with a quark matter component.

BCS-BEC crossover at finite temperature in the broken-symmetry phase

The BCS-BEC crossover is studied in a systematic way in the broken-symmetry phase between zero temperature and the critical temperature. This study bridges two regimes where quantum and thermal fluctuations are, respectively, important. The theory is implemented on physical grounds, by adopting a fermionic self-energy in the broken-symmetry phase that represents fermions coupled to superconducting fluctuations in weak coupling and to bosons described by the Bogoliubov theory in strong coupling. This extension of the theory beyond mean field proves important at finite temperature, to connect with the results in the normal phase. The order parameter, the chemical potential, and the single-particle spectral function are calculated numerically for a wide range of coupling and temperature. This enables us to assess the quantitative importance of superconducting fluctuations in the broken-symmetry phase over the whole BCS-BEC crossover. Our results are relevant to the possible realizations of this crossover with high-temperature cuprate superconductors and with ultracold fermionic atoms in a trap.

Scaling approach to itinerant quantum critical points

Based on phase space arguments, we develop a simple approach to metallic quantum critical points, designed to study the problem without integrating the fermions out of the partition function. The method is applied to the spin-fermion model of a T=0 ferromagnetic transition. Stability criteria for the conduction and the spin fluids are derived by scaling at the tree level. We conclude that anomalous exponents may be generated for the fermion self-energy and the spin-spin correlation functions below $d=3$, in spite of the spin fluid being above its upper critical dimension.

Pseudogaps in nested antiferromagnets

We analyze the fluctuation corrections to magnetic ordering in the case of a 3D antiferromagnet with flat Fermi surfaces, as physically realized in the case of chromium, and find that they are insufficient to produce a quantum critical point. This implies that the critical point observed in vandium doped chromium is due to a loss of nesting. We also derive the fermion self-energy in the paramagnetic phase and find that a pseudogap exists, though its magnitude is significantly reduced as compared to the spectral gap in the ordered state in the limit where the latter is small in comparison to the Fermi energy.

Power counting in relativistic baryon chiral perturbation theory

In the simple model of interacting pseudoscalar and fermion fields it is demonstrated that using an appropriately chosen renormalization condition one can have consistent power counting for multi-loop diagrams within the relativistic baryon chiral perturbation theory. Explicit calculations are performed for a two-loop diagram contributing to fermion self-energy.

Self-energy of improved staggered quarks

We calculate the fermion self-energy at $O({\ensuremath{\alpha}}_{s})$ for the Symanzik improved staggered fermion action used in recent lattice simulations by the MILC Collaboration. We demonstrate that the algebraic approach to lattice perturbation theory, suggested by us recently, is a powerful tool also for improved lattice actions.

Effect of gauge boson mass on chiral symmetry breaking in three-dimensional QED

In three-dimensional quantum electrodynamics (QED$_{3}$) with massive gauge boson, we investigate the Dyson-Schwinger equation for the fermion self-energy in the Landau gauge and find that chiral symmetry breaking (CSB) occurs when the gauge boson mass $\xi$ is smaller than a finite critical value $\xi_{cv}$ but is suppressed when $\xi > \xi_{cv}$. We further show that the critical value $\xi_{cv}$ does not qualitatively change after considering higher order corrections from the wave function renormalization and vertex function. Based on the relation between CSB and the gauge boson mass $\xi$, we give a field theoretical description of the competing antiferromagnetic and superconducting orders and, in particular, the coexistence of these two orders in high temperature superconductors. When the gauge boson mass $\xi$ is generated via instanton effect in a compact QED$_{3}$ of massless fermions, our result shows that CSB coexists with instanton effect in a wide region of $\xi$, which can be used to study the confinement-deconfinement phase transition.

Neutron resonance in the cuprates and its effect on fermionic excitations.

We argue that the exciton scenario for the magnetic resonance in the cuprate superconductors yields a small spectral weight of the resonance, in agreement with experiment. We show that the small weight is related to its concentration in a small region of momentum and energy. Despite this, we find that a large fermionic self-energy can indeed be generated by a resonance with such properties, i.e., the scattering from the resonance substantially affects the electronic properties of the cuprates below T(c).

Hypermagnetic field effects in the thermal bath of chiral fermions

The dispersion relations for leptons in the symmetric phase of the electroweak model in the presence of a constant hypermagnetic field are investigated. The one-loop fermion self-energies are calculated in the lowest Landau level approximation and used to show that the hypermagnetic field forbids the generation of the “effective mass” found as a pole of the fermions' propagators at high temperature and zero fields. In the considered approximation leptons behave as massless particles propagating only along the direction of the external field. The reported results can be of interest for the cosmological implications of primordial hypermagnetic fields.

Gauge-independent off-shell fermion self-energies at two loops: The cases of QED and QCD

We use the pinch technique formalism to construct the gauge-independent off-shell two-loop fermion self-energy, both for Abelian (QED) and non-Abelian (QCD) gauge theories. The new key observation is that all contributions originating from the longitudinal parts of gauge boson propagators, by virtue of the elementary tree-level Ward identities they trigger, give rise to effective vertices, which do not exist in the original Lagrangian; all such vertices cancel diagrammatically inside physical quantities, such as current correlation functions or S-matrix elements. We present two different, but complementary derivations: First, we explicitly track down the aforementioned cancellations inside two-loop diagrams, resorting to nothing more than basic algebraic manipulations. Second, we present an absorptive derivation, exploiting the unitarity of the S-matrix, and the Ward identities imposed on tree-level and one-loop physical amplitudes by gauge invariance, in the case of QED, or by the underlying Becchi-Rouet-Stora symmetry, in the case of QCD. The propagator-like sub-amplitude defined by means of this latter construction corresponds precisely to the imaginary parts of the effective self-energy obtained in the former case; the real part may be obtained from a (twice subtracted) dispersion relation. As in the one-loop case, the final two-loop fermion self-energy constructed using either method coincides with the conventional fermion self-energy computed in the Feynman gauge.

The fermion boson interaction within the linear sigma model at finite temperature

We reinvestigate the interaction of massless fermions with massless bosons at finite temperature. Specifically, we calculate the self-energy of massless fermions due the interaction with massless bosons at high temperature, which is the region where thermal effects are maximal. The calculations are concentrated in the limit of vanishing fermion three momentum and after considering the effective fermion and boson dressed masses, we obtain the damping rate of the fermion up to order g 3. It is shown that in the limit k 0⪡ T the fermion acquire a thermal mass of order gT and the leading term of the fermion damping rate is of order g 2 T+ g 3 T.

Remark on the momentum dependence of the magnetic catalysis in QED

We propose a new derivation of the fermion dynamical mass generated in four-dimensional QED in the presence of an external constant magnetic field, taking into account the momentum dependence of the fermion self-energy. The result confirms previous analytical studies, and we extend the computation to the finite temperature case where we find that the critical temperature is of the order of the dynamical mass at zero temperature.

Magnetic catalysis in three-dimensional QED at finite temperature: Beyond the constant mass approximation

We solve the Schwinger-Dyson equations for (2+1)-dimensional QED in the presence of a strong external magnetic field. The calculation is done at finite temperature and the fermionic self-energy is not supposed to be momentum independent, which is the usual simplification in such calculations. The phase diagram in the temperature-magnetic field plane is determined. For each value of the magnetic field the critical temperature is higher than in the constant mass approximation. In addition, the latter approximation shows a relative B independence of the critical temperature, which occurs for stronger magnetic fields in the momentum dependent case.

Fermion propagator in a nontrivial background field

We study the fermion propagator in a spatially varying classical background field, and show that, contrary to common wisdom, it may get nontrivial gradient corrections already at the first order in derivative expansion. This occurs whenever the fermion self-energy acquires a spatially (or temporally) varying pseudoscalar term, a simple example of which is given by a complex mass term m(x)= m_R + i gamma_5 m_I. Such effective mass terms arise for example in extensions of the Standard Model during the electroweak transition, and they are crucial in providing the CP-violation necessary for electroweak baryogenesis.

Dispersion relations in ultradegenerate relativistic plasmas

The propagation of excitation modes in a relativistic ultradegenerate plasma is modified by their interactions with the medium. These modifications can be computed by evaluating their on-shell self-energy, which gives (gauge-independent) dispersion relations. For modes with momentum close to the Fermi momentum, the one-loop fermion self-energy is dominated by a diagram with a soft photon in the loop. We find the one-loop dispersion relations for quasiparticles and antiquasiparticles, which behave differently as a consequence of their very different phase-space restrictions when they scatter with the electrons of the Fermi sea. In a relativistic system, the unscreened magnetic interactions spoil the normal Fermi-liquid behavior of the plasma. For small values of the Fermi velocity, we recover the nonrelativistic dispersion relations of condensed-matter systems.

DAMPING AND REACTION RATES AND WAVE FUNCTION RENORMALIZATION OF FERMIONS IN HOT GAUGE THEORIES

We examine the relation between the damping rate of a chiral fermion mode propagating in a hot plasma and the rate at which the mode approaches equilibrium. We show how these two quantities, obtained from the imaginary part of the fermion self-energy, are equal when the reaction rate is defined using the appropriate wave function of the mode in the medium. As an application, we compute the production rate of hard axions by Compton-like scattering processes in a hot QED plasma starting from both, the axion self-energy and the electron self-energy. We show that the latter rate coincides with the former only when this is computed using the corresponding medium spinor modes.

Radiative corrections for the gauged Thirring model in causal perturbation theory

We evaluate the one-loop fermion self-energy for the gauged Thirring model in (2+1) dimensions, with one massive fermion flavor, in the framework of the causal perturbation theory. In contrast to QED$_3$, the corresponding two-point function turns out to be infrared finite on the mass shell. Then, by means of a Ward identity, we derive the on-shell vertex correction and discuss the role played by causality for nonrenormalizable theories.

Fermionic dispersion relations at finite temperature and non-vanishing chemical potentials in the minimal standard model

We calculate the fermionic dispersion relations in the minimal standard model at finite temperature in presence of non-vanishing chemical potentials due to the CP-asymmetric fermionic background. The dispersion relations are calculated for a vacuum expectation value of the Higgs field equal to zero (unbroken electroweak symmetry). The calculation is performed in the real time formalism of the thermal field theory at one-loop order in a general $\xi$ gauge. The fermionic self-energy is calculated at leading order in temperature and chemical potential and this fact permits us to obtain gauge invariant analytical expressions for the dispersion relations.

Electronic Raman scattering in superconducting cuprates

We show that the novel features observed in Raman experiments on optimally doped and underdoped Bi-2212 compounds in B1g geometry can be explained by a strong fermionic self-energy due to the interaction with spin fluctuations. We compute the Raman intensity R(ω) both above and below Tc, and show that in both cases R(ω) progressively deviates, with decreasing doping, from that in a Fermi-gas due to increasing contribution from the fermionic self-energy. We also show that the final state interaction increases with decreasing doping and gradually transforms the 2Δ peak in the superconducting state into a pseudo resonance mode below 2Δ. We argue that these results agree well with the experimental data for Bi-2212.