Efficient calculation of imaginary time displaced correlation functions in the projector auxiliary field quantum Monte-Carlo algorithm

The calculation of imaginary time displaced correlation functions with the auxiliary field projector quantum Monte-Carlo algorithm provides valuable insight (such as spin and charge gaps) in the model under consideration. One of the authors and M. Imada [F.F. Assaad and M. Imada, J. Phys. Soc. Jpn. 65 189 (1996).] have proposed a numerically stable method to compute those quantities. Although precise this method is expensive in CPU time. Here, we present an alternative approach which is an order of magnitude quicker, just as precise, and very simple to implement. The method is based on the observation that for a given auxiliary field the equal time Green function matrix, $G$, is a projector: $G^2 = G$.Comment: 4 papes, 1 figure in eps forma

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

Image resonance in the many-body density of states at a metal surface

The electronic properties of a semi-infinite metal surface without a bulk gap are studied by a formalism that is able to account for the continuous spectrum of the system. The density of states at the surface is calculated within the GW approximation of many-body perturbation theory. We demonstrate the presence of an unoccupied surface resonance peaked at the position of the first image state. The resonance encompasses the whole Rydberg series of image states and cannot be resolved into individual peaks. Its origin is the shift in spectral weight when many-body correlation effects are taken into account

Stability of condensate in superconductors

According to the BCS theory the superconducting condensate develops in a single quantum mode and no Cooper pairs out of the condensate are assumed. Here we discuss a mechanism by which the successful mode inhibits condensation in neighboring modes and suppresses a creation of noncondensed Cooper pairs. It is shown that condensed and noncondensed Cooper pairs are separated by an energy gap which is smaller than the superconducting gap but large enough to prevent nucleation in all other modes and to eliminate effects of noncondensed Cooper pairs on properties of superconductors. Our result thus justifies basic assumptions of the BCS theory and confirms that the BCS condensate is stable with respect to two-particle excitations

Antiferromagnetism and single-particle properties in the two-dimensional half-filled Hubbard model: a non-linear sigma model approach

We describe a low-temperature approach to the two-dimensional half-filled Hubbard model which allows us to study both antiferromagnetism and single-particle properties. This approach ignores amplitude fluctuations of the antiferromagnetic (AF) order parameter and is valid below a crossover temperature $T_X$ which marks the onset of AF short-range order. Directional fluctuations (spin waves) are described by a non-linear sigma model (NL$\sigma$M) that we derive from the Hubbard model. At zero temperature and weak coupling, our results are typical of a Slater antiferromagnet. The AF gap is exponentially small; there are well-defined Bogoliubov quasi-particles (QP's) (carrying most of the spectral weight) coexisting with a high-energy incoherent excitation background. As $U$ increases, the Slater antiferromagnet progressively becomes a Mott-Heisenberg antiferromagnet. The Bogoliubov bands evolve into Mott-Hubbard bands separated by a large AF gap. A significant fraction of spectral weight is transferred from the Bogoliubov QP's to incoherent excitations. At finite temperature, there is a metal-insulator transition between a pseudogap phase at weak coupling and a Mott-Hubbard insulator at strong coupling. Finally, we point out that our results straightforwardly translate to the half-filled attractive Hubbard model, where the ${\bf q}=(\pi,\pi)$ charge and ${\bf q}=0$ pairing fluctuations combine to form an order parameter with SO(3) symmetry.Comment: Revtex4, 19 pages, 14 figures; (v2) final version as publishe

Hall Effect and Resistivity in High-Tc Superconductors: The Conserving Approximation

The Hall coefficient (R_H) of high-Tc cuprates in the normal state shows the striking non-Fermi liquid behavior: R_H follows a Curie-Weiss type temperature dependence, and |R_H|>>1/|ne| at low temperatures in the under-doped compounds. Moreover, R_H is positive for hole-doped compounds and is negative for electron-doped ones, although each of them has a similar hole-like Fermi surface. In this paper, we give the explanation of this long-standing problem from the standpoint of the nearly antiferromagnetic (AF) Fermi liquid. We consider seriously the vertex corrections for the current which are indispensable to satisfy the conservation laws, which are violated within the conventional Boltzmann transport approximation. The obtained total current J_k takes an enhanced value and is no more perpendicular to the Fermi surface due to the strong AF fluctuations. By virtue of this mechanism, the anomalous behavior of R_H in high-Tc cuprates is neutrally explained. We find that both the temperature and the (electron, or hole) doping dependences of R_H in high-T_c cuprates are reproduced well by numerical calculations based on the fluctuation-exchange (FLEX) approximation, applied to the single-band Hubbard model. We also discuss the temperature dependence of R_H in other nearly AF metals, e.g., V_2O_3, kappa-BEDT-TTF organic superconductors, and heavy fermion systems close to the AF phase boundary.Comment: 19 pages, to appear in Phys. Rev. B, No.59, Vol.22, 199

A real space auxiliary field approach to the BCS-BEC crossover

The BCS to BEC crossover in attractive Fermi systems is a prototype of weak to strong coupling evolution in many body physics. While extensive numerical results are available, and several approximate methods have been developed, most of these schemes are unsuccessful in the presence of spatial inhomogeneity. Such situations call for a real space approach that can handle large spatial scales and retain the crucial thermal fluctuations. With this in mind, we present comprehensive results of a real space auxiliary field approach to the BCS to BEC crossover in the attractive Hubbard model in two dimensions. The scheme reproduces the Hartree-Fock-Bogoliubov ground state, and leads to a $T_c$ scale that agrees with quantum Monte Carlo estimates to within a few percent. We provide results on the $T_c$, amplitude and phase fluctuations, density of states, and the momentum resolved spectral function over the entire interaction and temperature window. We suggest how the method generalises successfully to the presence of disorder, trapping, and population imbalance.Comment: This article supersedes arXiv:1105.115