We implement an explicit two-loop calculation of the coupling functions and the self-energy of interacting fermions with a two-dimensional flat Fermi surface in the framework of the field theoretical renormalization group ͑RG͒ approach. Throughout the calculation both the Fermi surface and the Fermi velocity are assumed to be fixed and unaffected by interactions. We show that in two dimensions, in a weak coupling regime, there is no significant change in the RG flow compared to the well-known one-loop results available in the literature. However, if we extrapolate the flow to a moderate coupling regime there are interesting new features associated with an anisotropic suppression of the quasiparticle weight Z along the Fermi surface, and the vanishing of the renormalized coupling functions for several choices of the external momenta.

We analyze the one-dimensional (1D) and the two-dimensional (2D) repulsive Hubbard models (HM) for densities slightly away from half-filling through the behavior of two central quantities of a system: the uniform charge and spin susceptibilities. We point out that a consistent renormalization group treatment of them can only be achieved within a two-loop approach or beyond. In the 1D HM, we show that this scheme reproduces correctly the metallic behavior given by the well-known Luttinger liquid fixed-point result. Then, we use the same approach to deal with the more complicated 2D HM. In this case, we are able to show that both uniform susceptibilities become suppressed for moderate interaction parameters as one take the system towards the Fermi surface. Therefore, this result adds further support to the interpretation that those systems are in fact insulating spin liquids. Later, we perform the same calculations in 2D using the conventional random phase approximation, and establish clearly a comparison between the two schemes.

We apply a functional implementation of the field-theoretical renormalization group (RG) method up to two loops to the single-impurity Anderson model. To achieve this, we follow a RG strategy similar to that proposed by Vojta et al. [Phys. Rev. Lett. 85, 4940 (2000)], which consists of defining a soft ultraviolet regulator in the space of Matsubara frequencies for the renormalized Green's function. Then we proceed to derive analytically and solve numerically integro-differential flow equations for the effective couplings and the quasiparticle weight of the present model, which fully treat the interplay of particle-particle and particle-hole parquet diagrams and the effect of the two-loop self-energy feedback into them. We show that our results correctly reproduce accurate numerical renormalization group data for weak to slightly moderate interactions. These results are in excellent agreement with other functional Wilsonian RG works available in the literature. Since the field-theoretical RG method turns out to be easier to implement at higher loops than the Wilsonian approach, higher-order calculations within the present approach could improve further the results for this model at stronger couplings. We argue that the present RG scheme could thus offer a possible alternative to other functional RG methods to describe electronic correlations within this model.

We present the formalism for a two-loop renormalization group ͑RG͒ calculation of some order-parameter susceptibilities associated with a two-dimensional ͑2D͒ flat Fermi-surface model. In this order of perturbation theory, one must take into account the self-energy effects directly in all RG flow equations. In one-loop order, our calculation reproduces the well-known results obtained previously by other RG schemes. That is, for repulsive interactions all susceptibilities diverge in the low-energy limit and the antiferromagnetic ͑AF͒ spindensity-wave correlations produce indeed the leading instability in the system. In contrast, in two-loop order, only the AF susceptibility diverges for this model. However, even this divergence takes place at a much slower rate than in the one-loop RG approach. The purpose of this paper is to show in a very simple setting how to assess the importance of two-loop quantum fluctuations in 2D interacting fermionic models. With some modifications, the present formalism can also be extended to discuss more realistic models such as the paradigmatic 2D Hubbard model.

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ABSTRACT:In this work, we present calculations of the vibrational energy levels of the H 2 ϩ and H 3 ϩ systems using the correlation function quantum Monte Carlo (CFQMC) and normal model analysis. The classical results are a qualitative first approximation of the normal modes. The results of the CFQMC calculations show the importance of the quantum effects as well as anharmonicity in these systems.

We calculate the charge compressibility and uniform spin susceptibility for the two-dimensional (2D) Hubbard model slightly away from half-filling within a two-loop renormalization group scheme. We find numerically that both those quantities flow to zero as we increase the initial interaction strength from weak to intermediate couplings. This result implies gap openings in both charge and spin excitation spectra for the latter interaction regime. When this occurs, the ground state of the lightly doped 2D Hubbard model may be interpreted as an insulating spin liquid as opposed to a Mott insulating state.PACS numbers: 71.10. Hf, 71.10.Pm, 71.27.+a After two decades of intensive research on the highTc superconductors, physicists are still puzzled by some of their very unusual electronic properties 1 . The prominent example is given by the cuprates. At zero doping, despite the fact that their highest occupied band is halffilled, they are charge insulators, and display antiferromagnetic long-range order. For this reason, they are said to be Mott insulators. As soon as one starts doping those compounds with holes, the long-range magnetic order becomes rapidly suppressed, and there are experimental evidences of an emergence of a spin gap in their corresponding excitation spectra 2 . A charge gap is also observed by ARPES experiments in such lightly-doped systems 3 . Moreover, at finite temperatures, they turn themselves into poor conductors with electronic properties differing considerably from the predictions of Landau's Fermi liquid theory. This scenario configures the so-called pseudogap regime. Although this phase continues to be not well understood, it is widely acknowledged to play a fundamental role in the underlying microscopic mechanism of such high-Tc superconductors. Indeed, upon some further doping, those poor metals become superconducting with d-wave symmetry up to relatively high temperatures around the optimal doping level.From the theoretical viewpoint, it is widely accepted that the appropriate model for describing such systems is the two-dimensional (2D) Hubbard model (HM), since it is known to have a Mott insulating phase at half-filling, and is expected to become a d-wave superconductor at larger doping 4 . However, its intermediate doping regime, which could provide some insight to understand the physical nature of the pseudogap state, still remains elusive to this date. In this Letter we intend to address this question using renormalization group (RG) techniques in order to infer about the ground state of such model for electron densities slightly away from the half-filling limit.Our considerations here will be based on a complete two-loop RG calculation of the uniform charge (CS) and spin (SS) susceptibilities of the 2D HM, taking into account simultaneously both the renormalization of the couplings, and the self-energy effects. (The CS is also called the charge compressibility of the system.) To best of our knowledge, it is the first time that such a full two-loop RG calculation is performed ...

We present a theoretical study on the detailed mechanism and kinetics of the H + HCN → H + HNC process. The potential energy surface was calculated at the complete basis set quantum chemical method, CBS-QB3. The vibrational frequencies and geometries for four isomers (H CN, cis-HCNH, trans-HCNH, CNH), and seven saddle points (TSn where n = 1 - 7) are very important and must be considered during the process of formation of the HNC in the reaction were calculated at the B3LYP/6-311G(2d,d,p) level, within CBS-QB3 method. Three different pathways (PW1, PW2, and PW3) were analyzed and the results from the potential energy surface calculations were used to solve the master equation. The results were employed to calculate the thermal rate constant and pathways branching ratio of the title reaction over the temperature range of 300 up to 3000 K. The rate constants for reaction H + HCN → H + HNC were fitted by the modified Arrhenius expressions. Our calculations indicate that the formation of the HNC preferentially occurs via formation of cis-HCNH, the fitted expression is k (T) = 9.98 × 10 T exp(-7.62 kcal.mol/R T) while the predicted overall rate constant k (T) = 9.45 × 10 T exp(-8.56 kcal.mol/R T) in cm molecule s . Graphical Abstract (a) Potential energy surface, (b) thermal rate constants as a function of temperature and