Weakly correlated electrons on a square lattice: a renormalization group theory

We study the weakly interacting Hubbard model on the square lattice using a one-loop renormalization group approach. The transition temperature T_c between the metallic and (nearly) ordered states is found. In the parquet regime, (T_c >> |mu|), the dominant correlations at temperatures below T_c are antiferromagnetic while in the BCS regime (T_c << |mu|) at T_c the d-wave singlet pairing susceptibility is most divergent.Comment: 12 pages, REVTEX, 3 figures included, submitted to Phys. Rev. Let

Phonons and d-wave pairing in the two-dimensional Hubbard model

We analyze the influence of phonons on the d-wave pairing instability in the Hubbard model on the two-dimensional square lattice at weak to moderate interaction U, using a functional renormalization group scheme with frequency-dependent interaction vertices. As measured by the pairing scale, the B1g buckling mode enhances the pairing, while other phonon modes decrease the pairing. When various phonon modes are included together, the net effect on the scale is small. However, in situations where d-wave superconductivity and other tendencies, e.g. antiferromagnetism, are closely competing, the combined effect of different phonons may be able to tip the balance towards pairing.Comment: 4 pages, 3 figure

d-wave superconductivity and Pomeranchuk instability in the two-dimensional Hubbard model

We present a systematic stability analysis for the two-dimensional Hubbard model, which is based on a new renormalization group method for interacting Fermi systems. The flow of effective interactions and susceptibilities confirms the expected existence of a d-wave pairing instability driven by antiferromagnetic spin fluctuations. More unexpectedly, we find that strong forward scattering interactions develop which may lead to a Pomeranchuk instability breaking the tetragonal symmetry of the Fermi surface.Comment: 4 pages (RevTeX), 4 eps figure

κ−(BEDT−TTF)2X\kappa-(BEDT-TTF)_2X organic crystals: superconducting versus antiferromagnetic instabilities in an anisotropic triangular lattice Hubbard model

A Hubbard model at half-filling on an anisotropic triangular lattice has been proposed as the minimal model to describe conducting layers of $\kappa-(BEDT-TTF)_2X$ organic materials. The model interpolates between the square lattice and decoupled chains. The $\kappa-(BEDT-TTF)_2X$ materials present many similarities with cuprates, such as the presence of unconventional metallic properties and the close proximity of superconducting and antiferromagnetic phases. As in the cuprates, spin fluctuations are expected to play a crucial role in the onset of superconductivity. We perform a weak-coupling renormalization-group analysis to show that a superconducting instability occurs. Frustration in the antiferromagnetic couplings, which arises from the underlying geometrical arrangement of the lattice, breaks the perfect nesting of the square lattice at half-filling. The spin-wave instability is suppressed and a superconducting instability predominates. For the isotropic triangular lattice, there are again signs of long-range magnetic order, in agreement with studies at strong-coupling.Comment: 4 pages, 5 eps figs, to appear in Can. J. Phys. (proceedings of the Highly Frustrated Magnetism (HFM-2000) conference, Waterloo, Canada, June 2000

Re-entrant hidden order at a metamagnetic quantum critical end point

Magnetization measurements of URu2Si2 in pulsed magnetic fields of 44 T reveal that the hidden order phase is destroyed before appearing in the form of a re-entrant phase between ~ 36 and 39 T. Evidence for conventional itinerant electron metamagnetism at higher temperatures suggests that the re-entrant phase is created in the vicinity of a quantum critical end point.Comment: 8 pages, including 3 figures (Physical Review Letters, in press) a systematic error in the field calibration has been fixed since the original submission of this manuscrip

Orbital quantization in the high magnetic field state of a charge-density-wave system

A superposition of the Pauli and orbital coupling of a high magnetic field to charge carriers in a charge-density-wave (CDW) system is proposed to give rise to transitions between subphases with quantized values of the CDW wavevector. By contrast to the purely orbital field-induced density-wave effects which require a strongly imperfect nesting of the Fermi surface, the new transitions can occur even if the Fermi surface is well nested at zero field. We suggest that such transitions are observed in the organic metal $\alpha$-(BEDT-TTF)$_2$KHg(SCN)$_4$ under a strongly tilted magnetic field.Comment: 14 pages including 4 figure

Magnetic and superconducting instabilities of the Hubbard model at the van Hove filling

We use a novel temperature-flow renormalization group technique to analyze magnetic and superconducting instabilities in the two-dimensional t-t' Hubbard model for particle densities close to the van Hove filling as a function of the next-nearest neighbor hopping t'. In the one-loop flow at the van Hove filling, the characteristic temperature for the flow to strong coupling is suppressed drastically around t'_c approx. -0.33t, suggesting a quantum critical point between d-wave pairing at moderate t'>t'_c and ferromagnetism for t'<t'_c. Upon increasing the particle density in the latter regime the leading instability occurs in the triplet pairing channel.Comment: 4 pages, to appear in Physical Review Letter

Effect of a lattice upon an interacting system of electrons: Breakdown of scaling and decay of persistent currents

For an interacting system of N electrons, we study the conditions under which a lattice model of size L with nearest neighbor hopping t and U/r Coulomb repulsion has the same ground state as a continuum model. For a fixed value of N, one gets identical results when the inter-electron spacing to the Bohr radius ratio r_s < r_s^*. Above r_s^*, the persistent current created by an enclosed flux begins to decay and r_s ceases to be the scaling parameter. Three criteria giving similar r_s^* are proposed and checked using square lattices.Comment: 7 pages, 5 postscript figure

Kohn-Luttinger instability of the t-t' Hubbard model in two dimensions: variational approach

An effective Hamiltonian for the Kohn-Luttinger superconductor is constructed and solved in the BCS approximation. The method is applied to the t-t' Hubbard model in two dimensions with the following results: (i) The superconducting phase diagram at half filling is shown to provide a weak-coupling analog of the recently proposed spin liquid state in the J_1-J_2 Heisenberg model. (ii) In the parameter region relevant for the cuprates we have found a nontrivial energy dependence of the gap function in the dominant d-wave pairing sector. The hot spot effect in the angular dependence of the superconducting gap is shown to be quite weak