Evolution of the pairing pseudogap in the spectral function with interplane anisotropy

We study the pairing pseudogap in the spectral function as a function of interplane coupling. The analytical expressions for the self-energy in the critical regime are obtained for any degree of anisotropy. The frequency dependence of the self-energy is found to be qualitatively different in two and three dimensions, and the crossover from two to three dimensional behavior is discussed. In particular, by considering the anisotropy of the Fermi velocity and gap along the Fermi surface, we can qualitatively explain recent photoemission experiments on high temperature superconductors concerning the temperature dependent Fermi arcs seen in the pseudogap phase.Comment: 20 pages, revtex, 5 encapsulated postscript figures include

Many-body Theory vs Simulations for the pseudogap in the Hubbard model

The opening of a critical-fluctuation induced pseudogap (or precursor pseudogap) in the one-particle spectral weight of the half-filled two-dimensional Hubbard model is discussed. This pseudogap, appearing in our Monte Carlo simulations, may be obtained from many-body techniques that use Green functions and vertex corrections that are at the same level of approximation. Self-consistent theories of the Eliashberg type (such as the Fluctuation Exchange Approximation) use renormalized Green functions and bare vertices in a context where there is no Migdal theorem. They do not find the pseudogap, in quantitative and qualitative disagreement with simulations, suggesting these methods are inadequate for this problem. Differences between precursor pseudogaps and strong-coupling pseudogaps are also discussed.Comment: Accepted, Phys. Rev. B15 15Mar00. Expanded version of original submission, Latex, 8 pages, epsfig, 5 eps figures (Last one new). Discussion on fluctuation and strong coupling induced pseudogaps expande

Role of symmetry and dimension on pseudogap phenomena

The attractive Hubbard model in d=2 is studied through Monte Carlo simulations at intermediate coupling. There is a crossover temperature $T_X$ where a pseudogap appears with concomitant precursors of Bogoliubov quasiparticles that are not local pairs. The pseudogap in $A(k,\omega)$ occurs in the renormalized classical regime when the correlation length is larger than the direction-dependent thermal de Broglie wave length, $\xi_{th}=\hbar v_{F}(k)/k_{B}T.$ The ratio $T_{X}/T_{c}$ for the pseudogap may be made arbitrarily large when the system is close to a point where the order parameter has SO(n) symmetry with n>2. This is relevant in the context of SO(5) theories of high $T_c$ but has more general applicability.Comment: 4 pages, LaTeX, 4 epsf figures included. Corrected to agree with published version. Main change, one new figur

Non-perturbative approach to the attractive Hubbard model

A non-perturbative approach to the single-band attractive Hubbard model is presented in the general context of functional derivative approaches to many-body theories. As in previous work on the repulsive model, the first step is based on a local-field type ansatz, on enforcement of the Pauli principle and a number of crucial sum-rules. The Mermin-Wagner theorem in two dimensions is automatically satisfied. At this level, two-particle self-consistency has been achieved. In the second step of the approximation, an improved expression for the self-energy is obtained by using the results of the first step in an exact expression for the self-energy where the high- and low-frequency behaviors appear separately. The result is a cooperon-like formula. The required vertex corrections are included in this self-energy expression, as required by the absence of a Migdal theorem for this problem. Other approaches to the attractive Hubbard model are critically compared. Physical consequences of the present approach and agreement with Monte Carlo simulations are demonstrated in the accompanying paper (following this one).Comment: Revtex, 19 page

Shadow features and shadow bands in the paramagnetic state of cuprate superconductors

The conditions for the precursors of antiferromagnetic bands in cuprate superconductors are studied using weak-to-intermediate coupling approach. It is shown that there are, in fact, three different precursor effects due to the proximity to antiferromagnetic instability: i) the shadow band which associated with new pole in the Green's function ii) the dispersive shadow feature due to the thermal enhancement of the scattering rate and iii) the non-dispersive shadow feature due to quantum spin fluctuation that exist only in $\vec{k}-$scan of the spectral function $A(\omega _{Fixed},\vec{k})$. I found that dispersive shadow peaks in $A(\omega,\vec{k})$ can exist at finite temperature T in the renormalized classical regime, when $T\gg \omega _{sf}$, $\xi_{AFM} >\xi_{th}=v_F/T$ ($\omega _{sf}$ is the characteristic energy of spin fluctuations, $\xi_{th}$ is the thermal wave length of electron). In contrast at zero temperature, only non-dispersive shadow feature in $A(\omega_{Fixed},\vec{k})$ has been found. I found, however, that the latter effect is always very small. The theory predict no shadow effects in the optimally doped materials. The conditions for which shadow peaks can be observed in photoemission are discussed.Comment: 6 pages, REVTEX, 2 ps figures, version to be published in PR

Self-Consistent Random Phase Approximation - Application to the Hubbard Model for finite number of sites

Within the 1D Hubbard model linear closed chains with various numbers of sites are considered in Self Consistent Random Phase Approximation (SCRPA). Excellent results with a minimal numerical effort are obtained for 2+4n sites cases, confirming earlier results with this theory for other models. However, the 4n sites cases need further considerations. SCRPA solves the two sites problem exactly. It therefore contains the two electrons and high density Fermi gas limits correctly.Comment: 17 pages, 17 figure

Spin fluctuations and pseudogap in the two-dimensional half-filled Hubbard model at weak coupling

Starting from the Hubbard model in the weak-coupling limit, we derive a spin-fermion model where the collective spin excitations are described by a non-linear sigma model. This result is used to compute the fermion spectral function $A({\bf k},\omega)$ in the low-temperature regime where the antiferromagnetic (AF) coherence length is exponentially large (``renormalized classical'' regime). At the Fermi level, $A({\bf k}_F,\omega)$ exhibits two peaks around $\pm\Delta_0$ (with $\Delta_0$ the mean-field gap), which are precursors of the zero-temperature AF bands, separated by a pseudogap.Comment: 6 pages, 2 figures, revised versio

Antiferromagnetism of the 2D Hubbard Model at Half Filling: Analytic Ground State at Weak Coupling

We introduce a local formalism to deal with the Hubbard model on a N times N square lattice (for even N) in terms of eigenstates of number operators, having well defined point symmetry. For U -> 0, the low lying shells of the kinetic energy are filled in the ground state. At half filling, using the 2N-2 one-body states of the partially occupied shell S_{hf}, we build a set of (2N-2 N-1)^{2} degenerate unperturbed ground states with S_{z}=0 which are then resolved by the Hubbard interaction \hat{W}=U\sum_{r}\hat{n}_{r\ua}\hat{n}_{r\da}. In S_{hf} we study the many-body eigenstates of the kinetic energy with vanishing eigenvalue of the Hubbard repulsion (W=0 states). In the S_{z}=0 sector, this is a N times degenerate multiplet. From the singlet component one obtains the ground state of the Hubbard model for U=0^{+}, which is unique in agreement with a theorem by Lieb. The wave function demonstrates an antiferromagnetic order, a lattice step translation being equivalent to a spin flip. We show that the total momentum vanishes, while the point symmetry is s or d for even or odd N/2, respectively.Comment: 13 pages, no figure

Theory of spin and charge fluctuations in the Hubbard model

A self-consistent theory of both spin and charge fluctuations in the Hubbard model is presented. It is in quantitative agreement with Monte Carlo data at least up to intermediate coupling $(U\sim 8t)$. It includes both short-wavelength quantum renormalization effects, and long-wavelength thermal fluctuations which can destroy long-range order in two dimensions. This last effect leads to a small energy scale, as often observed in high temperature superconductors. The theory is conserving, satisfies the Pauli principle and includes three-particle correlations necessary to account for the incipient Mott transition.Comment: J1K 2R1 10 pages, Revtex 3.0, 4 uuencoded postscript figures, report# CRPS-93-4

Pairing fluctuations and pseudogaps in the attractive Hubbard model

The two-dimensional attractive Hubbard model is studied in the weak to intermediate coupling regime by employing a non-perturbative approach. It is first shown that this approach is in quantitative agreement with Monte Carlo calculations for both single-particle and two-particle quantities. Both the density of states and the single-particle spectral weight show a pseudogap at the Fermi energy below some characteristic temperature T*, also in good agreement with quantum Monte Carlo calculations. The pseudogap is caused by critical pairing fluctuations in the low-temperature renormalized classical regime $\omega < T$ of the two-dimensional system. With increasing temperature the spectral weight fills in the pseudogap instead of closing it and the pseudogap appears earlier in the density of states than in the spectral function. Small temperature changes around T* can modify the spectral weight over frequency scales much larger than temperature. Several qualitative results for the s-wave case should remain true for d-wave superconductors.Comment: 20 pages, 12 figure