Beta function and anomaly of the Fermi surface for a d=1 system of interacting fermions in a periodic potential

We derive a perturbation theory, based on the renormalization group, for the Fermi surface of a one dimensional system of fermions in a periodic potential interacting via a short range, spin independent potential. The infrared problem is studied by writing the Schwinger functions in terms of running couplings. Their flow is described by a Beta function, whose existence and analyticity as a function of the running couplings is proved. If the fermions are spinless we prove that the Beta function is vanishing and the renormalization flow is bounded for any small interaction. If the fermions are spinning the Beta function is not vanishing but, if the conduction band is not filled or half filled and the interaction is repulsive, it is possible again to control the flow proving the partial asymptotic freedom of the theory. This is done showing that the Beta function is partially vanishing using the exact solution of the Mattis model, which is the spin analogue of the Luttinger model. In both these cases Schwinger functions are anomalous so that the system is a Luttinger liquid. Our results extend the work in [B.G.P.S.], where neither spin nor periodic potential were considered; an explicit proof of some technical results used but not explicitly proved there is also provided.     

Liquid–Vapor Phase Transitions for Systems with Finite-Range Interactions

We consider particles in ^d , d2, interacting via attractive pair and repulsive four-body potentials of the Kac type. Perturbing about mean-field theory, valid when the interaction range becomes infinite, we prove rigorously the existence of a liquid–gas phase transition when the interaction range is finite but long compared to the interparticle spacing for a range of temperature.     

Flow to strong coupling in the two-dimensional Hubbard model

We extend the analysis of the renormalization group flow in the two-dimensional Hubbard model close to half-filling using the recently developed temperature flow formalism. We investigate the interplay of d-density wave and Fermi surface deformation tendencies with those towards d-wave pairing and antiferromagnetism. For a ratio of next nearest to nearest neighbor hoppings, t'/t = - 0.25, and band fillings where the Fermi surface is inside the Umklapp surface, only the d-pairing susceptibility diverges at low temperatures. When the Fermi surface intersects the Umklapp surface close to the saddle points, d-wave pairing, d-density wave, antiferromagnetic and, to a weaker extent, d-wave Fermi surface deformation susceptibilities grow together when the interactions flow to strong coupling. We interpret these findings as indications for a non-trivial strongly coupled phase with short-ranged superconducting and antiferromagnetic correlations, in close analogy with the spin liquid ground state in the well-understood two-leg Hubbard ladder. Received 23 January 2002     

Markov and stability properties of equilibrium states for nearest-neighbor interactions

Consider models on the lattice ^d with finite spin space per lattice point and nearest-neighbor interaction. Under the condition that the transfer matrix is invertible we use a transfer-matrix formalism to show that each Gibbs state is determined by its restriction to any pair of adjacent (hyper)planes. Thus we prove that (also in multiphase regions) translationally invariant states have a global Markov property. The transfer-matrix formalism permits us to view the correlation functions of a classicald-dimensional system as obtained by a linear functional on a noncommutative (quantum) system in (d – 1)-dimensions. More precisely, for reflection positive classical states and an invertible transfer matrix the linear functional is a state. For such states there is a decomposition theory available implying statements on the ergodic decompositions of the classical state ind dimensions. In this way we show stability properties of _ev ^d -ergodic states and the absence of certain types of breaking of translational invariance.     

“W = 0” pairing in Cu-O clusters and in the plane

The Cu-O plane and the clusters that possess the same C_4v symmetry around a Cu ion have 2-hole eigenstates of the kinetic energy with vanishing on-site repulsion (W=0 pairs). Cluster calculations by exact diagonalisation show that these are the quasiparticles that lead to a paired ground state, and have superconducting flux-quantisation properties. Here, we extend the theory to the full plane, and show that the W=0 quasiparticles are again the natural explanation of superconducting flux-quantisation. Moreover, by a new approach which is exact in principle, we calculate the effective interaction between two holes added to the ground state of the repulsive three-band Hubbard model. To explain how a noninteracting electron gas becomes a superconductor when switching the local Coulomb interaction, we obtain a closed-form analytic expression including the effects of all virtual transitions to 4-body intermediate states (exchange of an electron-hole pair). Our scheme is ready to include other interactions which are not considered in the Hubbard model but may be important. In the plane, the W=0 pairs have ¹ B ₂ and ¹ A ₂ symmetry. The effective interaction in these channels is attractive and leads to a Cooper-like instability of the Fermi liquid, while it is repulsive for triplet pairs. From , we derive an integral equation for the pair eigenfunction; the binding energy of the pairs is in the range of tens of meV. However, our symmetry-based method is far more general than the model. Received 18 December 1998     

Ab initio calculation of the lifetime of quasiparticle excitations in transition metals within the framework of the <Emphasis Type="Italic">GW</Emphasis> approximation

This paper reports on the results of ab initio calculations of the lifetimes τ of quasiparticle excitations in cubic d transition metals (V, Nb, Ta, Mo, W, Rh, Ir) within the GW approximation, which represents the self-energy of quasiparticles by the product of the Green’s function and the dynamically screened Coulomb potential. A comparative analysis of the dependences of the lifetime τ(ω) on the excitation energy ω is performed, and the specific features of the dependences τ(ω) in going from metal to metal within a particular group and along the d periods are revealed. It is found that the dependence τ(ω) on the excitation energy differs from the dependence τ ～ ω^?2 obtained within the free-electron model and is primarily determined by the density of d states localized in the vicinity of the Fermi level and by the electron interaction screened by the d electrons.     

Spin-polaron nature of fermion quasiparticles and their <Emphasis Type="Italic">d</Emphasis>-wave pairing in cuprate superconductors

In the framework of the spin-fermion model, to which the Emery model is reduced in the limit of strong electron correlations, it is shown that the fermion quasiparticles in cuprate high-T _c superconductors (HTSCs) arise under a strong effect of exchange coupling between oxygen holes and spins of copper ions. This underlies the spin-polaron nature of fermion quasiparticles in cuprate HTSCs. The Cooper instability with respect to the d-wave symmetry of the order parameter is revealed for an ensemble of such quasiparticles. For the normal phase, the spin-polaron concept allows us to reproduce the fine details in the evolution of the Fermi surface with the changes in the doping level x observed in experiment for La_2-xSr_xCuO₄. The calculated T–x phase diagram correlates well with the available experimental data for cuprate HTSCs.     

Thed=2tJ model on a triangular lattice at large doping

We determine the spectra and interactions of quasiparticles in thed=2tJ model on a triangular lattice forJ2t and near 2/3 electron filling. We find coexistence of magnons and quasielectrons atJ=2t and a transition from repulsion among quasielectrons atJ<2t to attraction atJ>2t. The mathematical methods developed here involve graded cosets and are also applicable, in modified form, to the Fermi liquid regime of thetJ model on a square lattice.     

On the spectral problem for anyons

We consider the spectral problem resulting from the Schrödinger equation for a quantum system ofn2 indistinguishable, spinless, hard-core particles on a domain in two dimensional Euclidian space. For particles obeying fractional statistics, and interacting via a repulsive hard core potential, we provide a rigorous framework for analysing the spectral problem with its multi-valued wave functions.Partially supported by the Mathematical Sciences Research Institute, Berkeley California, under NSF Grant # DMS 8505550Partially supported under NSF Grant no. DMR-9101542     

A new aspect of superconductivity in A-15 compounds

We present a new aspect of superconductivity in A-15 compounds which is able to explain their exceptional role among the highT _c superconductors. The basic idea is that a strong energy dependence of the electronic density of states near the Fermi level may greatly reduce the repulsive part of the frequency dependent electron-phonon interaction. This leads to a large enhancement ofT _c which is a maximum when the Fermi energy is comparable to a typical phonon energy. Our findings are based on numerical solutions of the Eliashberg equations where both the retardation of the electron-phonon coupling and the energy dependence of the electronic density of states have been included. For the electronic density of states we use the models of Labbé und Friedel and of Cohen et al., while the shape of the Eliashberg function ² F() is taken from the tunneling results of Shen. We compare our theory to experimental results for ternary A-15 compounds.     

Unconventional superconductivity in low density electron systems and conventional superconductivity in hydrogen metallic alloys

In this short review, we first discuss the results, which are mainly devoted to the generalizations of the famous Kohn–Luttinger mechanism of superconductivity in purely repulsive fermion systems at low electron densities. In the context of repulsive-U Hubbard model and Shubin–Vonsovsky model we consider briefly the superconducting phase diagrams and the symmetries of the order parameter in novel strongly correlated electron systems including idealized monolayer and bilayer graphene. We stress that purely repulsive fermion systems are mainly the subject of unconventional low-temperature superconductivity. To get the high temperature superconductivity in cuprates (with T_C of the order of 100 K) we should proceed to the t–J model with the van der Waals interaction potential and the competition between short-range repulsion and long-range attraction. Finally we note that to describe superconductivity in metallic hydrogen alloys under pressure (with T_C of the order of 200 K) it is reasonable to reexamine more conventional mechanisms connected with electron–phonon interaction. These mechanisms arise in the attractive-U Hubbard model with static onsite or intersite attractive potential or in more realistic theories (which include retardation effects) such as Migdal–Eliashberg strong coupling theory or even Fermi–Bose mixture theory of Ranninger et al. and its generalizations.     

Long-range order in a simple model of interacting fermions

We consider a model of spinless fermions on a lattice, interacting through a nearest neighbor repulsion. In the half-filled band case and for dimensionsd 2, we rigorously prove that there is long-range order in some domain of the parameters=(k _B T)^–1 andt/U, wheret is the hopping amplitude of the particles,U the strength of their repulsion, and the inverse temperature. Our technique is based on the usual Peierls argument of classical statistical mechanics but fails for the groundstate. We discuss the specific difficulties introduced by the Fermi statistics.Work supported in part by U.S. NSF grant PHY 90-19433-A02.     

Effective interactions in dilute mixtures of3He in4He

Nonlocal pseudopotentials which describe the effective interaction between³He quasiparticles, and between these quasiparticles and the background⁴He liquid, are obtained as a function of concentration and pressure by generalizing the Aldrich-Pines pseudopotentials for pure³He and⁴He to dilute mixtures. The hierarchy of physical effects which determine these pseudopotentials is established. Interaction-induced short-range correlations are the dominant physical feature; next in order of importance is the greater zero point motion associated with the replacement of a⁴He atom by a³He atom, while spin-induced Pauli principle correlations play a significantly smaller, albeit still important role. We find a consistent trend in the change of the effective direct quasiparticle interactions with increasing concentration, and show how the Aldrich-Pines pseudopotentials for pure³He quasiparticles represent a natural extension of our results for dilute mixtures. Our calculated nonlocal pseudopotential for³He quasiparticles is qualitatively similar to that proposed by Bardeen, Baym, and Pines; it changes sign at somewhat lower momentum transfers than the BBP result, varies little with concentration, and provides a physical basis for understanding the BBP result. The effective interaction between quasiparticles of parallel spin, here determined for the first time, is essentially repulsive in the very dilute limit; as the concentration increases, it becomes increasingly attractive at low momentum transfers, and resembles closely that between antiparallel spin quasiparticles at 5% concentration. The concentration-dependent transport properties calculated from these pseudopotentials (which involve only one phenomenological parameter) are in good agreement with experiment at saturated vapor pressure (SVP), 10 atm, and 20 atm. Maxima in the thermal conductivity and spin diffusion are predicted to occur at concetrations somewhat less than 4%. Because the effective quasiparticle interactions are somewhat more repulsive than those previously proposed, we find the transition of the³He quasiparticles to the superfluid state takes place at significantly lower temperatures than many previous estimates; our predicted maximum superfluid transition temperature is 2×10^–8 K (for a 0.6% mixture at 20 atm).     

Occurrence of a Mott-like gap in single-particle spectra of electron systems possessing flat bands

An unconventional type of the Mott’s insulators where the gap in the spectrum of single-particle excitations is associated with repulsive effective interactions between quasiparticles is shown to exist in strongly correlated electron systems of solids that possess flat bands. The occurrence of this gap is demonstrated to be the consequence of violation of particle–hole symmetry, inherent in such systems. The results obtained are applied to elucidate the Fermi arc structure observed at temperatures up to 100 K in angle-resolved photoemission spectra of the compound Sr₂IrO₄, not showing superconductivity down to low T.     

Hyperfine interaction parameters and ground-state wavefunctions of vanadyl ion complexes

Using crystal field approach a theoretical estimate of the ground-state wavefunctions of vanadyl ion doped in various crystals have been made using ESR data and is found to bed _xy in our coordinate system with slight admixture of the excited states ,d _xz andd _yz. The hyperfine interaction parameterP and Fermi contact coupling parameterK have also been estimated for these vanadyl-doped crystals. Results agree with similar studies made earlier.     

Construction of the Hierarchical φ4-Trajectory

We study the invariant unstable manifold of the trivial renormalization-group fixed point tangent to the ⁴-vertex in the hierarchical approximation. We parametrize it by a running ⁴-coupling with linear step -function. The manifold is studied as a fixed point of the renormalization group composed with a flow of the running coupling. We present a rigorous construction of it beyond perturbation theory by means of a contraction mapping. Starting from a perturbative approximant of order seven, we obtain a convergent representation in dimensions 2 < D < 28/9 with certain restrictions. The perturbative approximant is logarithmically divergent in D = 3 dimensions.     

1/d corrections for interacting spinless fermions: One-particle properties

One-particle properties of the spinless fermion model with repulsion at half filling are calculated within an approach correct to first order in the inverse of the lattice dimensiond. Continuity of the limitd requires a scaling of the nearest-neighbour hopping proportional to and of the nearest-neighbour interaction proportional to 1/d. Due to this scaling the Hartree approximation becomes exact in infinite dimensions. We show that 1/d corrections comprise the Fock diagram and the local correlation diagram in the self-consistent Dyson equation. This approach is applied to simple-cubic systems in dimensiond=1, 2 and 3. Ground state properties and the charge-density wave phase diagram are calculated. AtT=0 the inclusion of 1/d terms gives only small corrections to the leading Hartree contribution ind=2, 3. ForT>0, however, the 1/d corrections are important. They lead to a non-negligible reduction of the critical temperature. Ind=1 the 1/d corrections are very large, but they do not succeed in removing the spurious phase transition atT>0. The 1/d approach provides a good and tractable approximation ind=3 and probably ind=2, which allows also further systematic improvement.     

A single-parameter trial wave function for the mixed valence ground state

The mixed valence trial ground state suggested by Stevens and Brandow is reconsidered in the case of two electrons per atom. The wellknown difficulties due to nonorthogonality are resolved by expanding the trial state in an orthonormal basis. The expansion coefficients are determinants composed of Bloch phase factors, as in the Gutzwiller method. Studying first the limiting case of the Kaplan-Mahanti strongly localized ground state in the Brandow formalism, we derive rules for a simplified handling of the determinants; this opens the way to the more complicated weakly localized ground state. This is handled by expressing theN variational parameters of the Brandow formalism through a single one, the hybridization temperature . The ground state energy is a well-behaved function of the hybridization matrix elementV. The valence and the shift of the Fermi level are calculated to lowest order inV. The band occupation numbers follow a Fermi distribution at temperature V. We argue that the ground state is insulating, with thed-electrons localized into large Wannier-type orbitals centered on the respectivef-holes, as envisaged by Stevens.     

Calculation of the intrinsic viscosity for dilute polymer solutions undergoing shear flow

Starting from a set of coupled Langevin equations describing the dynamics of flexible (Gaussian) polymer chains in the presence of hydrodynamic interactions and undergoing a weak shear flow, the stress tensor is determined using Kramers formula. With the aid of renormalization group techniques the steady state intrinsic viscosity is extracted toO() (4–d,d being the spatial dimensionality) and to lowest nontrivial order in the flow strength. Within the preaveraging approximation we find a numerically small effect of shear thinning.     

Destruction of the Fermi surface due to pseudogap fluctuations in strongly correlated systems

We generalize the dynamical-mean field theory (DMFT) by including into the DMFT equations dependence on the correlation length of the pseudogap fluctuations via the additional (momentum dependent) self-energy Σ_k. This self-energy describes nonlocal dynamical correlations induced by short-ranged collective SDW-like antiferromagnetic spin (or CDW-like charge) fluctuations. At high enough temperatures, these fluctuations can be viewed as a quenched Gaussian random field with finite correlation length. This generalized DMFT + Σ_k approach is used for the numerical solution of the weakly doped one-band Hubbard model with repulsive Coulomb interaction on a square lattice with nearest and next nearest neighbor hopping. The effective single impurity problem is solved by using a numerical renormalization group (NRG). Both types of strongly correlated metals, namely, (i) doped Mott insulator and (ii) the case of the bandwidth W ? U (U-value of local Coulomb interaction) are considered. By calculating profiles of the spectral densities for different parameters of the model, we demonstrate the qualitative picture of Fermi surface destruction and formation of Fermi arcs due to pseudogap fluctuations in qualitative agreement with the ARPES experiments. Blurring of the Fermi surface is enhanced with the growth of the Coulomb interaction.