The Dynamical Mean Field Theory phase space extension and critical properties of the finite temperature Mott transition

We consider the finite temperature metal-insulator transition in the half filled paramagnetic Hubbard model on the infinite dimensional Bethe lattice. A new method for calculating the Dynamical Mean Field Theory fixpoint surface in the phase diagram is presented and shown to be free from the convergence problems of standard forward recursion. The fixpoint equation is then analyzed using dynamical systems methods. On the fixpoint surface the eigenspectra of its Jacobian is used to characterize the hysteresis boundaries of the first order transition line and its second order critical end point. The critical point is shown to be a cusp catastrophe in the parameter space, opening a pitchfork bifurcation along the first order transition line, while the hysteresis boundaries are shown to be saddle-node bifurcations of two merging fixpoints. Using Landau theory the properties of the critical end point is determined and related to the critical eigenmode of the Jacobian. Our findings provide new insights into basic properties of this intensively studied transition.Comment: 11 pages, 12 figures, 1 tabl

Magnetic impurities in the one-dimensional spin-orbital model

Using one-dimensional spin-orbital model as a typical example of quantum spin systems with richer symmetries, we study the effect of an isolated impurity on its low energy dynamics in the gapless phase through bosonization and renormalization group methods. In the case of internal impurities, depending on the symmetry, the boundary fixed points can be either an open chain with a residual spin or (and) orbital triplet left behind, or a periodic chain. However, these two fixed points are indistinguishable in the sense that in both cases, the lead-correction-to-scaling boundary operators (LCBO) only show Fermi-liquid like corrections to thermodynamical quantities. (Except the possible Curie-like contributions from the residual moments in the latter cases.) In the case of external (Kondo) impurities, the boundary fixed points, depending on the sign of orbital couplings, can be either an open chain with an isolated orbital doublet due to Kondo screening or it will flow to an intermediate fixed point with the same LCBO as that of the two-channel Kondo problem. Comparison with the Kondo effect in one-dimensional (1D) Heisenberg spin chain and multi-band Hubbard models is also made.Comment: 7 pages, No figur

One-Dimensional Electron Liquid in an Antiferromagnetic Environment: Spin Gap from Magnetic Correlations

We study a one-dimensional electron liquid coupled by a weak spin-exchange interaction to an antiferromagnetic spin-S ladder with n legs. A perturbative renormalization group analysis in the semiclassical limit reveals the opening of a spin gap, driven by the local magnetic correlations on the ladder. The effect, which we argue is present for any gapful ladder or gapless ladder with $nS\gg 1$, is enhanced by the repulsive interaction among the conduction electrons but is insensitive to the sign of the spin exchange interaction with the ladder. Possible implications for the striped phases of the cuprates are discussed.Comment: 5 pages, 1 figure, to appear in Phys. Rev. Let

A systematic review of randomised controlled trials on the effectiveness of exercise programs on lumbo pelvic pain among postnatal women

Background: A substantial number of women tend to be affected by Lumbo Pelvic Pain (LPP) following child birth. Physical exercise is indicated as a beneficial method to relieve LPP, but individual studies appear to suggest mixed findings about its effectiveness. This systematic review aimed to synthesise evidence from randomised controlled trials on the effectiveness of exercise on LPP among postnatal women to inform policy, practice and future research. Methods: A systematic review was conducted of all randomised controlled trials published between January 1990 and July 2014, identified through a comprehensive search of following databases: PubMed, PEDro, Embase, Cinahl, Medline, SPORTDiscus, Cochrane Pregnancy and Childbirth Group’s Trials Register, and electronic libraries of authors’institutions. Randomised controlled trials were eligible for inclusion if the intervention comprised of postnatal exercise for women with LPP onset during pregnancy or within 3 months after delivery and the outcome measures included changes in LPP. Selected articles were assessed using the PEDro Scale for methodological quality and findings were synthesised narratively as meta-analysis was found to be inappropriate due to heterogeneity among included studies. Results: Four randomised controlled trials were included, involving 251 postnatal women. Three trials were rated as of ‘good’ methodological quality. All trials, except one, were at low risk of bias. The trials included physical exercise programs with varying components, differing modes of delivery, follow up times and outcome measures. Intervention in one trial, involving physical therapy with specific stabilising exercises, proved to be effective in reducing LPP intensity. An improvement in gluteal pain on the right side was reported in another trial and a significant difference in pain frequency in another. Conclusion: Our review indicates that only few randomised controlled trials have evaluated the effectiveness of exercise on LPP among postnatal women. There is also a great amount of variability across existing trials in the components of exercise programs, modes of delivery, follow up times and outcome measures. While there is some evidence to indicate the effectiveness of exercise for relieving LPP, further good quality trials are needed to ascertain the most effective elements of postnatal exercise programs suited for LPP treatment

Competing Orders in Coupled Luttinger Liquids

We consider the problem of two coupled Luttinger liquids both at half filling and at low doping levels, to investigate the problem of competing orders in quasi-one-dimensional strongly correlated systems. We use bosonization and renormalization group equations to investigate the phase diagrams, to determine the allowed phases and to establish approximate boundaries among them. Because of the chiral translation and reflection symmetry in the charge mode away from half filling, orders of charge density wave (CDW) and spin-Peierls (SP) diagonal current (DC) and $d$-density wave (DDW) form two doublets and thus can be at most quasi-long range ordered. At half-filling, umklapp terms break this symmetry down to a discrete group and thus Ising-type ordered phases appear as a result of spontaneous breaking of the residual symmetries. Quantum disordered Haldane phases are also found, with finite amplitudes of pairing orders and triplet counterparts of CDW, SP, DC and DDW. Relations with recent numerical results and implications to similar problems in two dimensions are discussed.Comment: 16 pages, 5 figures, 4 tables. Revised manuscript; a misprint in Eq. B3 has been corrected. The paper is already in print in PR

Metal-Kondo insulating transitions and transport in one dimension

We study two different metal-insulating transitions possibly occurring in one-dimensional Kondo lattices. First, we show how doping the pure Kondo lattice model in the strong-coupling limit, results in a Pokrovsky-Talapov transition. This produces a conducting state with a charge susceptibility diverging as the inverse of the doping, that seems in agreement with numerical datas. Second, in the weak-coupling region, Kondo insulating transitions arise due to the consequent renormalization of the backward Kondo scattering. Here, the interplay between Kondo effect and electron-electron interactions gives rise to significant phenomena in transport, in the high-temperature delocalized (ballistic) regime. For repulsive interactions, as a perfect signature of Kondo localization, the conductivity is found to decrease monotonically with temperature. When interactions become attractive, spin fluctuations in the electron (Luttinger-type) liquid are suddenly lowered. The latter is less localized by magnetic impurities than for the repulsive counterpart, and as a result a large jump in the Drude weight and a maximum in the conductivity arise in the entrance of the Kondo insulating phase. These can be viewed as remnants of s-wave superconductivity arising for attractive enough interactions. Comparisons with transport in the single impurity model are also performed. We finally discuss the case of randomly distributed magnetic defects, and the applications on persistent currents of mesoscopic rings.Comment: 21 pages, two columns, 5 figures and 1 table; Final version: To appear in Physical Review

Scaling and criticality of the Kondo effect in a Luttinger liquid

A quantum Monte Carlo simulation method has been developed and applied to study the critical behavior of a single Kondo impurity in a Luttinger liquid. This numerically exact method has no finite-size limitations and allows to simulate the whole temperature range. Focusing on the impurity magnetic susceptibility, we determine the scaling functions, in particular for temperatures well below the Kondo temperature. In the absence of elastic potential scattering, we find Fermi-liquid behavior for strong electron-electron interactions, g_c < 1/2, and anomalous power laws for 1/2<g_c < 1, where g_c is the correlation parameter of the Luttinger liquid. These findings resolve a recent controversy. If elastic potential scattering is present, we find a logarithmically divergent impurity susceptibility at g_c<1/2 which can be rationalized in terms of the two-channel Kondo model.Comment: 11 pages REVTeX, incl. 9 PS figures, subm. to PR

Mid-Infrared Conductivity from Mid-Gap States Associated with Charge Stripes

The optical conductivity of La(2-x)Sr(x)NiO(4) has been interpreted in various ways, but so far the proposed interpretations have neglected the fact that the holes doped into the NiO(2) planes order in diagonal stripes, as established by neutron and X-ray scattering. Here we present a study of optical conductivity in La(2)NiO(4+d) with d=2/15, a material in which the charge stripes order three-dimensionally. We show that the conductivity can be decomposed into two components, a mid-infrared peak that we attribute to transitions from the filled valence band into empty mid-gap states associated with the stripes, and a Drude peak that appears at higher temperatures as carriers are thermally excited into the mid-gap states. The shift of the mid-IR peak to lower energy with increasing temperature is explained in terms of the Franck-Condon effect. The relevance of these results to understanding the optical conductivity in the cuprates is discussed.Comment: final version of paper (minor changes from previous version

Nodal quasi-particles and coexisting orders in striped superconductors

We study the properties of a quasi-one dimensional superconductor which consists of an alternating array of two inequivalent chains. This model is a simple charicature of a locally striped high temperature superconductor, and is more generally a theoretically controllable system in which the superconducting state emerges from a non-Fermi liquid normal state. Even in this limit, ``d-wave like'' order parameter symmetry is natural, but the superconducting state can either have a complete gap in the quasi-particle spectrum, or gapless ``nodal'' quasiparticles. We also find circumstances in which antiferromagnetic order (typically incommensurate) coexists with superconductivity.Comment: 4 pages, 1 figure, 1 table new version; vastly improved figure captio

Pairing and Density Correlations of Stripe Electrons in a Two-Dimensional Antiferromagnet

We study a one-dimensional electron liquid embedded in a 2D antiferromagnetic insulator, and coupled to it via a weak antiferromagnetic spin exchange interaction. We argue that this model may qualitatively capture the physics of a single charge stripe in the cuprates on length- and time scales shorter than those set by its fluctuation dynamics. Using a local mean-field approach we identify the low-energy effective theory that describes the electronic spin sector of the stripe as that of a sine-Gordon model. We determine its phases via a perturbative renormalization group analysis. For realistic values of the model parameters we obtain a phase characterized by enhanced spin density and composite charge density wave correlations, coexisting with subleading triplet and composite singlet pairing correlations. This result is shown to be independent of the spatial orientation of the stripe on the square lattice. Slow transverse fluctuations of the stripes tend to suppress the density correlations, thus promoting the pairing instabilities. The largest amplitudes for the composite instabilities appear when the stripe forms an antiphase domain wall in the antiferromagnet. For twisted spin alignments the amplitudes decrease and leave room for a new type of composite pairing correlation, breaking parity but preserving time reversal symmetry.Comment: Revtex, 28 pages incl. 5 figure