Alfredo Raya

QCD phase diagram from finite energy sum rules

We study the QCD phase diagram at finite temperature and baryon chemical potential by relating the behavior of the light-quark condensate to the threshold energy for the onset of perturbative QCD. These parameters are connected to the chiral symmetry restoration and the deconfinement phase transition, respectively. This relation is obtained in the framework of finite energy QCD sum rules at finite temperature and density, with input from Schwinger-Dyson methods to determine the light-quark condensate. Results indicate that both critical temperatures are basically the same within some 3% accuracy. We also obtain bounds for the position of the critical end point, mu_{B c} >~ 300 MeV and T_c <~ 185 MeV.

The electron propagator in external electromagnetic fields in low dimensions

We study the electron propagator in quantum electrodynamics in one and two spatial dimensions in the presence of external electromagnetic fields. In this case, the propagator is not diagonal in momentum space. We obtain the propagator on the basis of the eigenfunctions of the operator (γ⋅Π)2 in terms of which the propagator acquires a free form. Πμ is the canonical momentum operator and γμ are the Dirac matrices. In two dimensions, we work with an irreducible representation of the Clifford algebra and consider to all orders the effects of an arbitrary magnetic field perpendicular to the plane of motion of the electrons. We then discuss the special cases of a uniform magnetic field and an exponentially damped static magnetic field. These cases are relevant to graphene in the massless limit. We further consider the electron propagator for the massive Schwinger model and incorporate the effects of a constant electric field to all orders.

Chiral Symmetry Breaking and Confinement Beyond Rainbow-Ladder Truncation

A non-perturbative construction of the 3-point fermion-boson vertex which obeys its Ward-Takahashi or Slavnov-Taylor identity, ensures the massless fermion and boson propagators transform according to their local gauge covariance relations, reproduces perturbation theory in the weak coupling regime and provides a gauge independent description for dynamical chiral symmetry breaking (DCSB) and confinement has been a long-standing goal in physically relevant gauge theories such as quantum electrodynamics (QED) and quantum chromodynamics (QCD). In this paper, we demonstrate that the same simple and practical form of the vertex can achieve these objectives not only in 4-dimensional quenched QED (qQED4) but also in its 3-dimensional counterpart (qQED3). Employing this convenient form of the vertex emph{ansatz} into the Schwinger-Dyson equation (SDE) for the fermion propagator, we observe that it renders the critical coupling in qQED4 markedly gauge independent in contrast with the bare vertex and improves on the well-known Curtis-Pennington construction. Furthermore, our proposal yields gauge independent order parameters for confinement and DCSB in qQED3.

Thermomagnetic properties of the strong coupling in the local Nambu-Jona-Lasinio model

We study the thermomagnetic properties of the strong coupling constant G and quark mass M entering the Nambu-Jona-Lasinio model. For this purpose, we compute the quark condensate and compare it to lattice QCD (LQCD) results to extract the behavior of G and M as functions of the magnetic field strength and temperature. We find that at zero temperature, where the LQCD condensate is found to monotonically increase with the field strength, M also increases whereas G remains approximately constant. However, for temperatures above the chiral/deconfinement phase transitions, where the LQCD condensate is found to monotonically decrease with increasing field, M and G also decrease monotonically. For finite temperatures, below the transition temperature, we find that both G and M initially grow and then decrease with increasing field strength. To study possible consequences of the extracted temperature and magnetic field dependence of G and M, we compute the pressure and compare to LQCD results, finding an excellent qualitative agreement. In particular, we show that the transverse pressure, as a function of the field strength, is always negative for temperatures below the transition temperature whereas it starts off being positive and then becomes negative for temperatures above the transition temperature, also in agreement with LQCD results. We also show that for the longitudinal pressure to agree with LQCD calculations, the system should be described as a diamagnet. We argue that the turnover of M and G as functions of temperature and field strength is a key element that drives the behavior of the quark condensate going across the transition temperature and provides clues for a better understanding of the inverse magnetic catalysis phenomenon.

Thermomagnetic correlation lengths of strongly interacting matter in the Nambu-Jona-Lasinio model

We study the correlation length between test quarks with the same electric and color charges in the Nambu--Jona-Lasinio model, considering thermal and magnetic effects. We extract the correlation length from the quark correlation function. The latter is constructed from the probability amplitude to bring a given quark into the plasma, once a previous one with the same quantum numbers is placed at a given distance apart. For temperatures below the transition temperature, the correlation length starts growing as the field strength increases to then decrease for large magnetic fields. For temperatures above the critical temperature, the correlation length continues increasing as the field strength increases. We found that such behavior can be understood as a competition between the tightening induced by the classical magnetic force versus the random thermal motion. For large enough temperatures, the increase of the occupation number contributes to the screening of the interaction between the test particles. The growth of the correlation distance with the magnetic field can be understood as due to the closer proximity between one of the test quarks and the ones popped up from vacuum, which in turn appear due to the increase of the occupation number with temperature.

Electric current generation in distorted graphene

Graphene-like materials can be effectively described by quantum electrodynamics in (2+1) dimensions, QED3. In a pristine state, these systems exhibit a symmetry between the nonequivalent Dirac points in the honeycomb lattice. Realistic samples which include distortions and crystalline anisotropies are considered through mass gaps of topological and dynamical nature. In this work, we show that the incorporation of an in-plane uniform external magnetic field on this pseudochiral asymmetric configuration generates a nondissipative electric current aligned with the magnetic field: The pseudochiral magnetic effect (PCME). This scenario resembles the chiral magnetic effect in quantum chromodynamics (QCD).

Planar Dirac Fermions in External Electromagnetic Fields

We study the electron propagator in two spatial dimensions in the presence of external electromagnetic fields, this is, we focus in (2+1)-dimensional quantum electrodynamics (QED), where a third spatial dimension is suppressed. This is not a mere theoretical simplification, and we explain ourselves: back in time, some twenty years ago, it was shown that the low-energy effective theory of graphene in a tight-binding approach is the theory of two species of massless Dirac electrons in a (2+1)-dimensional Minkowski spacetime, each on a different irreducible representation of the Clifford algebra. The isolation of graphene samples in 2004 and 2005, has given rise to the new paradigm of relativistic condensed matter, bringing a new boost, both theoretical and experimental, to the matching of common interests of the condensedmatter and high energy physics communities. Thus, themassless limit of our findings is of direct relevance in this subject. We assume the electrons moving in a magnetic field alone pointing perpendicularly to their plane of motion. We first develop the general case and then, we present a couple of examples: themotion of electrons in a uniformmagnetic field, which is a canonical example to present the Ritusmethod and the case of a static magnetic field which decays exponentially along the x-axis (Murguia et al, 2010; Raya & Reyes, 2010). There are many problems relating electrons in non-uniform magnetic fields of relevance in graphene. In particular, it has been established the possibility to confine quasiparticles in magnetic barriers (DeMartino et al, 2007; Ramezani et al, 2009). This could be feasible creating spatially inhomogeneous, but constant in time, magnetic fields depositing ferromagnetic layers over the substrate of a graphene sample layer (Reijniers et al, 2001). The physical properties of graphene make it a promising novel material to control the transport properties in nanodevices. It has been considered to be used in electronics and spintronics applications, like in single-electron transistors (Ponomarenko et al, 2008; Wu et al, 2008), in the so called magnetic edge states (Park & Sim, 2008), which may play an important role in the spin-polarized currents along magnetic domains, and in quantum dots and antidots magnetically confined. Moreover, the quantum Hall effect in graphene has been observed at room temperature (Novoselov et al, 2007), evidence which confirms the great potential of graphene as the material to be used in carbon-based electronic devices. The effects of the exponentially decaying magnetic field can hardly be considered with other approaches, 13

Light absorption in distorted graphene

We model the low energy dynamics of graphene in the continuum in terms of a version of reduced quantum electrodynamics (QED) restricting fermions to a (2 + 1)-dimensional brane, while photons remain within the (3 + 1)-dimensional bulk. For charge carriers, besides the Dirac mass gap, we consider a Haldane mass term which is induced by parametrizing an effective parity 𝒫 and time-reversal 𝒯 symmetry breaking that occurs on the brane when distortions of the honeycomb array are such that the equivalence between sublattices is lost. We make use of the relativistic Kubo formula and carry out an explicit calculation of the transverse conductivity. As expected, the filling factor is a half (in natural units) for each fermion species. Furthermore, assuming that a sample of this material is radiated perpendicularly with polarized monochromatic light of frequency ω, from the modified Maxwell’s equations we address the problem of light absorption in graphene in terms of the said conductivity. We observe that light penetrating the sample changes its angle of polarization solely by effect of the induced mass, in analogy to the Faraday effect but in absence of magnetic fields. This effect might be relevant for the development of optic filters based on mechanical stretching of graphene flakes.

Confinement in Maxwell-Chern-Simons Planar Quantum Electrodynamics and the 1/N approximation

We study the analytical structure of the fermion propagator in planar quantum electrodynamics coupled to a Chern-Simons term within a four-component spinor formalism. The dynamical generation of parity-preserving and parity-violating fermion mass terms is considered, through the solution of the corresponding Schwinger-Dyson equation for the fermion propagator at leading order of the 1/N approximation in Landau gauge. The theory undergoes a first-order phase transition toward chiral symmetry restoration when the Chern-Simons coefficient {theta} reaches a critical value which depends upon the number of fermion families considered. Parity-violating masses, however, are generated for arbitrarily large values of the said coefficient. On the confinement scenario, complete charge screening - characteristic of the 1/N approximation - is observed in the entire (N,{theta})-plane through the local and global properties of the vector part of the fermion propagator.

Dynamical mass generation in strongly coupled quantum electrodynamics with weak magnetic fields

We study the dynamical generation of masses for fundamental fermions in quenched quantum electrodynamics in the presence of weak magnetic fields using Schwinger-Dyson equations. Contrary to the case where the magnetic field is strong, in the weak field limit the coupling should exceed certain critical value in order for the generation of masses to take place, just as in the case where no magnetic field is present. The weak field limit is defined as eB<<m(0){sup 2}, where m(0) is the value of the dynamically generated mass in the absence of the field. We carry out a numerical analysis to study the magnetic field dependence of the mass function above critical coupling and show that in this regime the dynamically generated mass and the chiral condensate for the lowest Landau level increase proportionally to (eB){sup 2}.