Phonon-mediated tuning of instabilities in the Hubbard model at half-filling

We obtain the phase diagram of the half-filled two-dimensional Hubbard model on a square lattice in the presence of Einstein phonons. We find that the interplay between the instantaneous electron-electron repulsion and electron-phonon interaction leads to new phases. In particular, a d$_{x^2-y^2}$-wave superconducting phase emerges when both anisotropic phonons and repulsive Hubbard interaction are present. For large electron-phonon couplings, charge-density-wave and s-wave superconducting regions also appear in the phase diagram, and the widths of these regions are strongly dependent on the phonon frequency, indicating that retardation effects play an important role. Since at half-filling the Fermi surface is nested, spin-density-wave is recovered when the repulsive interaction dominates. We employ a functional multiscale renormalization-group method that includes both electron-electron and electron-phonon interactions, and take retardation effects fully into account.Comment: 8 pages, 5 figure

Skyrmion Lattice in a Chiral Magnet

Skyrmions represent topologically stable field configurations with particle-like properties. We used neutron scattering to observe the spontaneous formation of a two-dimensional lattice of skyrmion lines, a type of magnetic vortices, in the chiral itinerant-electron magnet MnSi. The skyrmion lattice stabilizes at the border between paramagnetism and long-range helimagnetic order perpendicular to a small applied magnetic field regardless of the direction of the magnetic field relative to the atomic lattice. Our study experimentally establishes magnetic materials lacking inversion symmetry as an arena for new forms of crystalline order composed of topologically stable spin states

Electronic instabilities of a Hubbard model approached as a large array of coupled chains: competition between d-wave superconductivity and pseudogap phase

We study the electronic instabilities in a 2D Hubbard model where one of the dimensions has a finite width, so that it can be considered as a large array of coupled chains. The finite transverse size of the system gives rise to a discrete string of Fermi points, with respective electron fields that, due to their mutual interaction, acquire anomalous scaling dimensions depending on the point of the string. Using bosonization methods, we show that the anomalous scaling dimensions vanish when the number of coupled chains goes to infinity, implying the Fermi liquid behavior of a 2D system in that limit. However, when the Fermi level is at the Van Hove singularity arising from the saddle points of the 2D dispersion, backscattering and Cooper-pair scattering lead to the breakdown of the metallic behavior at low energies. These interactions are taken into account through their renormalization group scaling, studying in turn their influence on the nonperturbative bosonization of the model. We show that, at a certain low-energy scale, the anomalous electron dimension diverges at the Fermi points closer to the saddle points of the 2D dispersion. The d-wave superconducting correlations become also large at low energies, but their growth is cut off as the suppression of fermion excitations takes place first, extending progressively along the Fermi points towards the diagonals of the 2D Brillouin zone. We stress that this effect arises from the vanishing of the charge stiffness at the Fermi points, characterizing a critical behavior that is well captured within our nonperturbative approach.Comment: 13 pages, 7 figure

Solution of the infinite range t-J model

The t-J model with constant t and J between any pair of sites is studied by exploiting the symmetry of the Hamiltonian with respect to site permutations. For a given number of electrons and a given total spin the exchange term simply yields an additive constant. Therefore the real problem is to diagonalize the "t- model", or equivalently the infinite U Hubbard Hamiltonian. Using extensively the properties of the permutation group, we are able to find explicitly both the energy eigenvalues and eigenstates, labeled according to spin quantum numbers and Young diagrams. As a corollary we also obtain the degenerate ground states of the finite $U$ Hubbard model with infinite range hopping -t>0.Comment: 15 pages, 2 figure

Variational ground states of the two-dimensional Hubbard model

Recent refinements of analytical and numerical methods have improved our understanding of the ground-state phase diagram of the two-dimensional (2D) Hubbard model. Here we focus on variational approaches, but comparisons with both Quantum Cluster and Gaussian Monte Carlo methods are also made. Our own ansatz leads to an antiferromagnetic ground state at half filling with a slightly reduced staggered order parameter (as compared to simple mean-field theory). Away from half filling, we find d-wave superconductivity, but confined to densities where the Fermi surface passes through the antiferromagnetic zone boundary (if hopping between both nearest-neighbour and next-nearest-neighbour sites is considered). Our results agree surprisingly well with recent numerical studies using the Quantum Cluster method. An interesting trend is found by comparing gap parameters (antiferromagnetic or superconducting) obtained with different variational wave functions. They vary by an order of magnitude and thus cannot be taken as a characteristic energy scale. In contrast, the order parameter is much less sensitive to the degree of sophistication of the variational schemes, at least at and near half filling.Comment: 18 pages, 4 figures, to be published in New J. Phy

spl(2,1) dynamical supersymmetry and suppression of ferromagnetism in flat band double-exchange models

The low energy spectrum of the ferromagnetic Kondo lattice model on a N-site complete graph extended with on-site repulsion is obtained from the underlying spl(2,1) algebra properties in the strong coupling limit. The ferromagnetic ground state is realized for 1 and N+1 electrons only. We identify the large density of states to be responsible for the suppression of the ferromagnetic state and argue that a similar situation is encountered in the Kagome, pyrochlore, and other lattices with flat bands in their one-particle density of states.Comment: 7 pages, 1 figur

Collective fields in the functional renormalization group for fermions, Ward identities, and the exact solution of the Tomonaga-Luttinger model

We develop a new formulation of the functional renormalization group (RG) for interacting fermions. Our approach unifies the purely fermionic formulation based on the Grassmannian functional integral, which has been used in recent years by many authors, with the traditional Wilsonian RG approach to quantum systems pioneered by Hertz [Phys. Rev. B 14, 1165 (1976)], which attempts to describe the infrared behavior of the system in terms of an effective bosonic theory associated with the soft modes of the underlying fermionic problem. In our approach, we decouple the interaction by means of a suitable Hubbard-Stratonovich transformation (following the Hertz-approach), but do not eliminate the fermions; instead, we derive an exact hierarchy of RG flow equations for the irreducible vertices of the resulting coupled field theory involving both fermionic and bosonic fields. The freedom of choosing a momentum transfer cutoff for the bosonic soft modes in addition to the usual band cutoff for the fermions opens the possibility of new RG schemes. In particular, we show how the exact solution of the Tomonaga-Luttinger model emerges from the functional RG if one works with a momentum transfer cutoff. Then the Ward identities associated with the local particle conservation at each Fermi point are valid at every stage of the RG flow and provide a solution of an infinite hierarchy of flow equations for the irreducible vertices. The RG flow equation for the irreducible single-particle self-energy can then be closed and can be reduced to a linear integro-differential equation, the solution of which yields the result familiar from bosonization. We suggest new truncation schemes of the exact hierarchy of flow equations, which might be useful even outside the weak coupling regime.Comment: 27 pages, 15 figures; published version, some typos correcte

Exact integral equation for the renormalized Fermi surface

The true Fermi surface of a fermionic many-body system can be viewed as a fixed point manifold of the renormalization group (RG). Within the framework of the exact functional RG we show that the fixed point condition implies an exact integral equation for the counterterm which is needed for a self-consistent calculation of the Fermi surface. In the simplest approximation, our integral equation reduces to the self-consistent Hartree-Fock equation for the counterterm.Comment: 5 pages, 1 figur

Van Hove singularity and spontaneous Fermi surface symmetry breaking in Sr3Ru2O7

The most salient features observed around a metamagnetic transition in Sr3Ru2O7 are well captured in a simple model for spontaneous Fermi surface symmetry breaking under a magnetic field, without invoking a putative quantum critical point. The Fermi surface symmetry breaking happens in both a majority and a minority spin band but with a different magnitude of the order parameter, when either band is tuned close to van Hove filling by the magnetic field. The transition is second order for high temperature T and changes into first order for low T. The first order transition is accompanied by a metamagnetic transition. The uniform magnetic susceptibility and the specific heat coefficient show strong T dependence, especially a log T divergence at van Hove filling. The Fermi surface instability then cuts off such non-Fermi liquid behavior and gives rise to a cusp in the susceptibility and a specific heat jump at the transition temperature.Comment: 11 pages, 4 figure

On a global differential geometric approach to the rational mechanics of deformable media

In the past the rational mechanics of deformable media was largely concerned with materials governed by linear constitutive equations. In recent years, the theory has expanded considerably towards covering materials for which the constitutive equations are inherently nonlinear, and/or whose mechanical properties resemble in some respects those of a fluid and in others those of a solid. In the present article we formulate a satisfactory global mathematical theory of moving deformable media, which includes all these aspects