Field dependence of the magnetic spectrum in anisotropic and Dzyaloshinskii-Moriya antiferromagnets: I. Theory

We consider theoretically the effects of an applied uniform magnetic field on the magnetic spectrum of anisotropic two-dimensional and Dzyaloshinskii-Moriya layered quantum Heisenberg antiferromagnets. The first case is relevant for systems such as the two-dimensional square lattice antiferromagnet Sr(2)CuO(2)Cl(2), while the later is known to be relevant to the physics of the layered orthorhombic antiferromagnet La(2)CuO(4). We first establish the correspondence betwenn the low-energy spectrum obtained within the anisotropic non-linear sigma model and by means of the spin-wave approximation for a standard easy-axis antiferromagent. Then, we focus on the field-theory approach to calculate the magnetic field dependence of the magnon gaps and spectral intensities for magnetic fields applied along the three possible crystallographic directions. We discuss the various possible ground states and their evolution with temperature for the different field orientations, and the occurrence of spin-flop transitions for fields perpendicular to the layers (transverse fields) as well as for fields along the easy axis (longitudinal fields). Measurements of the one-magnon Raman spectrum in Sr(2)CuO(2)Cl(2) and La(2)CuO(4) and a comparison between the experimental results and the predictions of the present theory will be reported in part II of this research work [L. Benfatto et al., cond-mat/0602664].Comment: 21 pages, 11 figures, final version. Part II of the present work is presented in cond-mat/060266

Robustness of the optical-conductivity sum rule in Bilayer Graphene

We calculate the optical sum associated with the in-plane conductivity of a graphene bilayer. A bilayer asymmetry gap generated in a field-effect device can split apart valence and conduction bands, which otherwise would meet at two K points in the Brillouin zone. In this way one can go from a compensated semimetal to a semiconductor with a tunable gap. However, the sum rule turns out to be 'protected' against the opening of this semiconducting gap, in contrast to the large variations observed in other systems where the gap is induced by strong correlation effects.Comment: 6 pages, 3 figures. Final versio

Gap and pseudogap evolution within the charge-ordering scenario for superconducting cuprates

We describe the spectral properties of underdoped cuprates as resulting from a momentum-dependent pseudogap in the normal state spectrum. Such a model accounts, within a BCS approach, for the doping dependence of the critical temperature and for the two-parameter leading-edge shift observed in the cuprates. By introducing a phenomenological temperature dependence of the pseudogap, which finds a natural interpretation within the stripe quantum-critical-point scenario for high-T_c superconductors, we reproduce also the T_c-T^* bifurcation near optimum doping. Finally, we briefly discuss the different role of the gap and the pseudogap in determining the spectral and thermodynamical properties of the model at low temperatures.Comment: 13 pages (EPY style), 7 enclosed figures, to appear on Eur. Phys. J.

Extended scaling relations for planar lattice models

It is widely believed that the critical properties of several planar lattice models, like the Eight Vertex or the Ashkin-Teller models, are well described by an effective Quantum Field Theory obtained as formal scaling limit. On the basis of this assumption several extended scaling relations among their indices were conjectured. We prove the validity of some of them, among which the ones by Kadanoff, [K], and by Luther and Peschel, [LP].Comment: 32 pages, 7 fi

Coherence length in superconductors from weak to strong coupling

We study the evolution of the superconducting coherence length $\xi_0$ from weak to strong coupling, both within a s-wave and a d-wave lattice model. We show that the identification of $\xi_0$ with the Cooper-pair size $\xi_{pair}$ in the weak-coupling regime is meaningful only for a fully-gapped (e.g., s-wave) superconductor. Instead in the d-wave superconductor, where $\xi_{pair}$ diverges, we show that $\xi_0$ is properly defined as the characteristic length scale for the correlation function of the modulus of the superconducting order parameter. The strong-coupling regime is quite intriguing, since the interplay between particle-particle and particle-hole channel is no more negligible. In the case of s-wave pairing, which allows for an analytical treatment, we show that $\xi_0$ is of order of the lattice spacing at finite densities. In the diluted regime $\xi_0$ diverges, recovering the behavior of the coherence length of a weakly interacting effective bosonic system. Similar results are expected to hold for d-wave superconductors.Comment: 11 pages, 5 figures. Two appendices and new references adde

The low-energy phase-only action in a superconductor: a comparison with the XY model

The derivation of the effective theory for the phase degrees of freedom in a superconductor is still, to some extent, an open issue. It is commonly assumed that the classical XY model and its quantum generalizations can be exploited as effective phase-only models. In the quantum regime, however, this assumption leads to spurious results, such as the violation of the Galilean invariance in the continuum model. Starting from a general microscopic model, in this paper we explicitly derive the effective low-energy theory for the phase, up to fourth-order terms. This expansion allows us to properly take into account dynamic effects beyond the Gaussian level, both in the continuum and in the lattice model. After evaluating the one-loop correction to the superfluid density we critically discuss the qualitative and quantitative differences between the results obtained within the quantum XY model and within the correct low-energy theory, both in the case of s-wave and d-wave symmetry of the superconducting order parameter. Specifically, we find dynamic anharmonic vertices, which are absent in the quantum XY model, and are crucial to restore Galilean invariance in the continuum model. As far as the more realistic lattice model is concerned, in the weak-to-intermediate-coupling regime we find that the phase-fluctuation effects are quantitatively reduced with respect to the XY model. On the other hand, in the strong-coupling regime we show that the correspondence between the microscopically derived action and the quantum XY model is recovered, except for the low-density regime.Comment: 29 pages, 11 figures. Slightly revised presentation, accepted for publication in Phys. Rev.

Theory of fluctuation conductivity from interband pairing in pnictide superconductors

We derive the effective action for superconducting fluctuations in a four-band model for pnictides, discussing the emergence of a single critical mode out of a dominant interband pairing mechanism. We then apply our model to calculate the paraconductivity in two-dimensional and layered three-dimensional systems, and compare our results with recent resistivity measurements in SmFeAsOFComment: 4 pages, 1 figure; final versio

Frequency-dependent Thermal Response of the Charge System and Restricted Sum Rules in La(2-x)Sr(x)CuO(4)

By using new and previous measurements of the $ab$-plane conductivity $\sigma_1^{ab} (\omega,T)$ of La$_{2-x}$Sr$_x$CuO$_{4}$ (LSCO) it is shown that the spectral weight $W = \int_0^\Omega {\sigma_1^{ab} (\omega,T) d\omega}$ obeys the same law $W = W_0 - B(\Omega) T^2$ which holds for a conventional metal like gold, for $\Omega$'s below the plasma frequency. However $B(\Omega)$, which measures the "thermal response" of the charge system, in LSCO exhibits a peculiar behavior which points towards correlation effects. In terms of hopping models, $B(\Omega)$ is directly related to an energy scale $t_T$, smaller by one order of magnitude than the full bandwidth $t_0 \sim W_0$.Comment: 4 pages with 3 fig

Anomalous behavior in an effective model of graphene with Coulomb interactions

We analyze by exact Renormalization Group (RG) methods the infrared properties of an effective model of graphene, in which two-dimensional massless Dirac fermions propagating with a velocity smaller than the speed of light interact with a three-dimensional quantum electromagnetic field. The fermionic correlation functions are written as series in the running coupling constants, with finite coefficients that admit explicit bounds at all orders. The implementation of Ward Identities in the RG scheme implies that the effective charges tend to a line of fixed points. At small momenta, the quasi-particle weight tends to zero and the effective Fermi velocity tends to a finite value. These limits are approached with a power law behavior characterized by non-universal critical exponents.Comment: 42 pages, 7 figures; minor corrections, one appendix added (Appendix A). To appear in Ann. Henri Poincar

Functional Integral Construction of the Thirring model: axioms verification and massless limit

We construct a QFT for the Thirring model for any value of the mass in a functional integral approach, by proving that a set of Grassmann integrals converges, as the cutoffs are removed and for a proper choice of the bare parameters, to a set of Schwinger functions verifying the Osterwalder-Schrader axioms. The corresponding Ward Identities have anomalies which are not linear in the coupling and which violate the anomaly non-renormalization property. Additional anomalies are present in the closed equation for the interacting propagator, obtained by combining a Schwinger-Dyson equation with Ward Identities.Comment: 55 pages, 9 figure