Antiferromagnetic integer-spin chains in a staggered magnetic field: approaching the thermodynamic limit through the infinite-size DMRG

We investigate the behavior of antiferromagnetic integer-spin chains in a staggered magnetic field, by means of the density-matrix renormalization group, carefully addressing the role of finite-size effects within the Haldane phase at small fields. In the case of spin S=2, we determine the dependence of the groundstate energy and magnetization on the external field, in the thermodynamic limit, and show how the peculiar finite-size behavior can be connected with the crossover in the groundstate from a spin liquid to a polarized N\'eel state.Comment: 7 pages, 5 figure

Luttinger liquid, singular interaction and quantum criticality in cuprate materials

With particular reference to the role of the renormalization group approach and Ward identities, we start by recalling some old features of the one-dimensional Luttinger liquid as the prototype of non-Fermi-liquid behavior. Its dimensional crossover to the Landau normal Fermi liquid implies that a non-Fermi liquid, as, e.g., the normal phase of the cuprate high temperature superconductors, can be maintained in d>1, only in the presence of a sufficiently singular effective interaction among the charge carriers. This is the case when, nearby an instability, the interaction is mediated by fluctuations. We are then led to introduce the specific case of superconductivity in cuprates as an example of avoided quantum criticality. We will disentangle the fluctuations which act as mediators of singular electron-electron interaction, enlightening the possible order competing with superconductivity and a mechanism for the non-Fermi-liquid behavior of the metallic phase. This paper is not meant to be a comprehensive review. Many important contributions will not be considered. We will also avoid using extensive technicalities and making full calculations for which we refer to the original papers and to the many good available reviews. We will here only follow one line of reasoning which guided our research activity in this field.Comment: 23 pages, 10 figure

Spectroscopic evidences of quantum critical charge fluctuations in cuprates

We calculate the optical conductivity in a clean system of quasiparticles coupled to charge-ordering collective modes. The absorption induced by these modes may produce an anomalous frequency and temperature dependence of low-energy optical absorption in some cuprates. However, the coupling with lattice degrees of freedom introduces a non-universal energy scale leading to scaling violation in low-temperature optical conductivity.Comment: Proceedings of M2S 2006. To appear in Physica

Intrinsic instability of electronic interfaces with strong Rashba coupling

We consider a model for the two-dimensional electron gas formed at the interface of oxide heterostructures, which includes a Rashba spin-orbit coupling proportional to the electric field perpendicular to the interface. Based on the standard mechanism of polarity catastrophe, we assume that the electric field is proportional to the electron density. Under these simple and general assumptions, we show that a phase separation instability occurs for realistic values of the spin-orbit coupling and of the band parameters. This could provide an intrinsic mechanism for the recently observed inhomogeneous phases at the LaAlO_3/SrTiO_3 or LaTiO_3/SrTiO_3 interfaces.Comment: 5 pages, 4 figure

Renormalization group and Ward identities in quantum liquid phases and in unconventional critical phenomena

By reviewing the application of the renormalization group to different theoretical problems, we emphasize the role played by the general symmetry properties in identifying the relevant running variables describing the behavior of a given physical system. In particular, we show how the constraints due to the Ward identities, which implement the conservation laws associated with the various symmetries, help to minimize the number of independent running variables. This use of the Ward identities is examined both in the case of a stable phase and of a critical phenomenon. In the first case we consider the problems of interacting fermions and bosons. In one dimension general and specific Ward identities are sufficient to show the non-Fermi-liquid character of the interacting fermion system, and also allow to describe the crossover to a Fermi liquid above one dimension. This crossover is examined both in the absence and presence of singular interaction. On the other hand, in the case of interacting bosons in the superfluid phase, the implementation of the Ward identities provides the asymptotically exact description of the acoustic low-energy excitation spectrum, and clarifies the subtle mechanism of how this is realized below and above three dimensions. As a critical phenomenon, we discuss the disorder-driven metal-insulator transition in a disordered interacting Fermi system. In this case, through the use of Ward identities, one is able to associate all the disorder effects to renormalizations of the Landau parameters. As a consequence, the occurrence of a metal-insulator transition is described as a critical breakdown of a Fermi liquid.Comment: 47 pages, 11 figure

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.