Universality relations in non-solvable quantum spin chains

We prove the exact relations between the critical exponents and the susceptibility, implied by the Haldane Luttinger liquid conjecture, for a generic lattice fermionic model or a quantum spin chain with short range weak interaction. The validity of such relations was only checked in some special solvable models, but there was up to now no proof of their validity in non-solvable models

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

Renormalization Group and Asymptotic Spin--Charge separation for Chiral Luttinger liquids

The phenomenon of Spin-Charge separation in non-Fermi liquids is well understood only in certain solvable d=1 fermionic systems. In this paper we furnish the first example of asymptotic Spin-Charge separation in a d=1 non solvable model. This goal is achieved using Renormalization Group approach combined with Ward-Identities and Schwinger-Dyson equations, corrected by the presence of a bandwidth cut-offs. Such methods, contrary to bosonization, could be in principle applied also to lattice or higher dimensional systems.Comment: 45 pages, 11 figure

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

On the application of Mattis-Bardeen theory in strongly disordered superconductors

The low energy optical conductivity of conventional superconductors is usually well described by Mattis-Bardeen (MB) theory which predicts the onset of absorption above an energy corresponding to twice the superconducing (SC) gap parameter Delta. Recent experiments on strongly disordered superconductors have challenged the application of the MB formulas due to the occurrence of additional spectral weight at low energies below 2Delta. Here we identify three crucial items which have to be included in the analysis of optical-conductivity data for these systems: (a) the correct identification of the optical threshold in the Mattis-Bardeen theory, and its relation with the gap value extracted from the measured density of states, (b) the gauge-invariant evaluation of the current-current response function, needed to account for the optical absorption by SC collective modes, and (c) the inclusion into the MB formula of the energy dependence of the density of states present already above Tc. By computing the optical conductvity in the disordered attractive Hubbard model we analyze the relevance of all these items, and we provide a compelling scheme for the analysis and interpretation of the optical data in real materials.Comment: 11 pages, 6 figure

Fermi liquid behavior in the 2D Hubbard model at low temperatures

We prove that the weak coupling 2D Hubbard model away from half filling is a Landau Fermi liquid up to exponentially small temperatures. In particular we show that the wave function renormalization is an order 1 constant and essentially temperature independent in the considered range of temperatures and that the interacting Fermi surface is a regular convex curve. This result is obtained by deriving a convergent expansion (which is not a power series) for the two point Schwinger function by Renormalization Group methods and proving at each order suitable power counting improvements due to the convexity of the interacting Fermi surface. Convergence follows from determinant bounds for the fermionic expectations.Comment: 66 pages, 10 figure

An Approximate KAM-Renormalization-Group Scheme for Hamiltonian Systems

We construct an approximate renormalization scheme for Hamiltonian systems with two degrees of freedom. This scheme is a combination of Kolmogorov-Arnold-Moser (KAM) theory and renormalization-group techniques. It makes the connection between the approximate renormalization procedure derived by Escande and Doveil, and a systematic expansion of the transformation. In particular, we show that the two main approximations, consisting in keeping only the quadratic terms in the actions and the two main resonances, keep the essential information on the threshold of the breakup of invariant tori.Comment: 6 pages, RevTe