On the correct continuum limit of the functional-integral representation for the four-slave-boson approach to the Hubbard model: Paramagnetic phase

The Hubbard model with finite on-site repulsion U is studied via the functional-integral formulation of the four-slave-boson approach by Kotliar and Ruckenstein. It is shown that a correct treatment of the continuum imaginary time limit (which is required by the very definition of the functional integral) modifies the free energy when fluctuation (1/N) corrections beyond mean-field are considered. Our analysis requires us to suitably interpret the Kotliar and Ruckenstein choice for the bosonic hopping operator and to abandon the commonly used normal-ordering prescription, in order to obtain meaningful fluctuation corrections. In this way we recover the exact solution at U=0 not only at the mean-field level but also at the next order in 1/N. In addition, we consider alternative choices for the bosonic hopping operator and test them numerically for a simple two-site model for which the exact solution is readily available for any U. We also discuss how the 1/N expansion can be formally generalized to the four-slave-boson approach, and provide a simplified prescription to obtain the additional terms in the free energy which result at the order 1/N from the correct continuum limit.Comment: Changes: Printing problems (due to non-standard macros) have been removed, 44 page

Phase separation and competition of superconductivity and magnetism in the two-dimensional Hubbard model: From strong to weak coupling

Cooperation and competition between the antiferromagnetic, d-wave superconducting and Mott-insulating states are explored for the two-dimensional Hubbard model including nearest and next-nearest-neighbor hoppings at zero temperature. Using the variational cluster approach with clusters of different shapes and sizes up to 10 sites, it is found that the doping-driven transition from a phase with microscopic coexistence of antiferromagnetism and superconductivity to a purely superconducting phase is discontinuous for strong interaction and accompanied by phase separation. At half-filling the system is in an antiferromagnetic Mott-insulating state with vanishing charge compressibility. Upon decreasing the interaction strength U below a certain critical value of roughly U=4 (in units of the nearest-neighbor hopping), however, the filling-dependent magnetic transition changes its character and becomes continuous. Phase separation or, more carefully, the tendency towards the formation of inhomogeneous states disappears. This critical value is in contrast to previous studies, where a much larger value was obtained. Moreover, we find that the system at half-filling undergoes the Mott transition from an insulator to a state with a finite charge compressibility at essentially the same value. The weakly correlated state at half-filling exhibits superconductivity microscopically admixed to the antiferromagnetic order. This scenario suggests a close relation between phase separation and the Mott-insulator physics.Comment: 7 pages, 8 figures, revised version to be published in Phys. Rev.

Correlated band structure of electron-doped cuprate materials

We present a numerical study of the doping dependence of the spectral function of the n-type cuprates. Using a variational cluster-perturbation theory approach based upon the self-energy-functional theory, the spectral function of the electron-doped two-dimensional Hubbard model is calculated. The model includes the next-nearest neighbor electronic hopping amplitude $t'$ and a fixed on-site interaction $U=8t$ at half filling and doping levels ranging from $x=0.077$ to $x=0.20$. Our results support the fact that a comprehensive description of the single-particle spectrum of electron-doped cuprates requires a proper treatment of strong electronic correlations. In contrast to previous weak-coupling approaches, we obtain a consistent description of the ARPES experiments without the need to introduce a doping-dependent on-site interaction $U$.Comment: 7 pages 4 eps figure

Variational Cluster Perturbation Theory for Bose-Hubbard models

We discuss the application of the variational cluster perturbation theory (VCPT) to the Mott-insulator--to--superfluid transition in the Bose-Hubbard model. We show how the VCPT can be formulated in such a way that it gives a translation invariant excitation spectrum -- free of spurious gaps -- despite the fact that if formally breaks translation invariance. The phase diagram and the single-particle Green function in the insulating phase are obtained for one-dimensional systems. When the chemical potential of the cluster is taken as a variational parameter, the VCPT reproduces the dimension dependence of the phase diagram even for one-site clusters. We find a good quantitative agreement with the results of the density-matrix renormalization group when the number of sites in the cluster becomes of order 10. The extension of the method to the superfluid phase is discussed.Comment: v1) 10 pages, 6 figures. v2) Final version as publishe

Phase diagram and single-particle spectrum of CuO2_2 layers within a variational cluster approach to the 3-band Hubbard model

We carry out a detailed numerical study of the three-band Hubbard model in the underdoped region both in the hole- as well as in the electron-doped case by means of the variational cluster approach. Both the phase diagram and the low-energy single-particle spectrum are very similar to recent results for the single-band Hubbard model with next-nearest-neighbor hoppings. In particular, we obtain a mixed antiferromagnetic+superconducting phase at low doping with a first-order transition to a pure superconducting phase accompanied by phase separation. In the single-particle spectrum a clear Zhang-Rice singlet band with an incoherent and a coherent part can be seen, in which holes enter upon doping around $(\pi/2,\pi/2)$. The latter is very similar to the coherent quasi-particle band crossing the Fermi surface in the single-band model. Doped electrons go instead into the upper Hubbard band, first filling the regions of the Brillouin zone around $(\pi,0)$. This fact can be related to the enhanced robustness of the antiferromagnetic phase as a function of electron doping compared to hole doping.Comment: 14 pages, 15 eps figure

Variational cluster approach to the Hubbard model: Phase-separation tendency and finite-size effects

Using the variational cluster approach (VCA), we study the transition from the antiferromagnetic to the superconducting phase of the two-dimensional Hubbard model at zero temperature. Our calculations are based on a new method to evaluate the VCA grand potential which employs a modified Lanczos algorithm and avoids integrations over the real or imaginary frequency axis. Thereby, very accurate results are possible for cluster sizes not accessible to full diagonalization. This is important for an improved treatment of short-range correlations, including correlations between Cooper pairs in particular. We investigate the cluster-size dependence of the phase-separation tendency that has been proposed recently on the basis of calculations for smaller clusters. It is shown that the energy barrier driving the phase separation decreases with increasing cluster size. This supports the conjecture that the ground state exhibits microscopic inhomogeneities rather than macroscopic phase separation. The evolution of the single-particle spectum as a function of doping is studied in addtion and the relevance of our results for experimental findings is pointed out.Comment: 7 pages, 6 figures, published versio

Extended self-energy functional approach for strongly-correlated lattice bosons in the superfluid phase

Among the various numerical techniques to study the physics of strongly correlated quantum many-body systems, the self-energy functional approach (SFA) has become increasingly important. In its previous form, however, SFA is not applicable to Bose-Einstein condensation or superfluidity. In this paper we show how to overcome this shortcoming. To this end we identify an appropriate quantity, which we term $D$, that represents the correlation correction of the condensate order parameter, as it does the self-energy for the Green's function. An appropriate functional is derived, which is stationary at the exact physical realizations of $D$ and of the self-energy. Its derivation is based on a functional-integral representation of the grand potential followed by an appropriate sequence of Legendre transformations. The approach is not perturbative and therefore applicable to a wide range of models with local interactions. We show that the variational cluster approach based on the extended self-energy functional is equivalent to the "pseudoparticle" approach introduced in Phys. Rev. B, 83, 134507 (2011). We present results for the superfluid density in the two-dimensional Bose-Hubbard model, which show a remarkable agreement with those of Quantum-Monte-Carlo calculations.Comment: 1 additional figure showing the region close to the tip of the Mott lobe, minor changes in the tex