Eberth Correa

Field-theoretical renormalization group for a flat two-dimensional Fermi surface

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 (RG) 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

Insulating spin liquid in the lightly doped two-dimensional Hubbard model

Z

Renormalization group calculation of the uniform susceptibilities in low-dimensional systems

along the Fermi surface, and the vanishing of the renormalized coupling functions for several choices of the external momenta.

Fermi surface renormalization and quantum confinement in the two-coupled chains model

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.

Theoretical study of the H + HCN → H + HNC process

We analyse the one-dimensional (1D) and the two-dimensional (2D) repulsive Hubbard models (HM) for densities slightly away from half-filling through the behaviour 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 behaviour 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 takes 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.

SUPERCONDUCTIVITY IN THE 2D ATTRACTIVE HUBBARD MODEL WITHIN A FUNCTIONAL FIELD-THEORETICAL RG

We address the problem of the Fermi surface renormalization and the quantum confinement regime (QCR) in the two coupled chains model (TCCM) of spinless fermions. We perform a self-consistent calculation of the renormalization group (RG) flows of the renormalized TCCM couplings and quasiparticle weight. On top of that we take explicitly into account the renormalization of the Fermi surface. The flow of the difference of the renormalized Fermi wave vectors associated with the bonding and antibonding bands has a dramatic effect on the single particle spectrum. Although the quasiparticle amplitude is nullified already at intermediate coupling the QCR is only observed at strong coupling. The state associated with this regime has a charge gap and it is not a Luttinger liquid. In contrast, the Fermi liquid regime is stabilized by the umklapp “g2-like” interactions at very weak coupling regime.

Breakdown of the Fermi-liquid regime in the two-dimensional Hubbard model from a two-loop field-theoretical renormalization group approach

AbstractWe 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 (H2CN, cis-HCNH, trans-HCNH, CNH2), 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 kPW2(T) = 9.98 × 10−22T2.41 exp(−7.62 kcal.mol−1/RT) while the predicted overall rate constant kOverall(T) = 9.45 × 10−21T2.15 exp(−8.56 kcal.mol−1/RT) in cm3 molecule−1s−1. Graphical Abstract(a) Potential energy surface, (b) thermal rate constants as a function of temperature and (c) the branching ratios (%) of PW1, PW2, PW3 pathways involved in rm H + HCN → H + HNC process.

Quantum and classical study of vibrational states of H +2 and H +3 molecules

We apply the functional field-theoretical renormalization group methodology up to two-loop order to the 2D attractive Hubbard model for weak bare interaction. Since the momentum-resolved quasiparticle weight ZΛ(p) is always close to unity in the RG flow, higher-order quantum fluctuations do not affect crucially the low-energy dynamics in this case. As a result, we observe a s-wave singlet superconducting quasi-long-range order phase as a function of doping in good agreement with other numerical methods. To assess the role played by the fluctuations we compare the critical temperature Tc in which the quasi-long-range superconducting order phase takes place within our approach with mean-field theory and quantum Monte Carlo results.