716 research outputs found
Zero-temperature Phase Diagram of Two Dimensional Hubbard Model
We investigate the two-dimensional Hubbard model on the triangular lattice
with anisotropic hopping integrals at half filling. By means of a self-energy
functional approach, we discuss how stable the non-magnetic state is against
magnetically ordered states in the system. We present the zero-temperature
phase diagram, where the normal metallic state competes with magnetically
ordered states with and structures. It is shown
that a non-magnetic Mott insulating state is not realized as the ground state,
in the present framework, but as a meta-stable state near the magnetically
ordered phase with structure.Comment: 4 pages, 4 figure
Two-site dynamical mean-field theory
It is shown that a minimum realization of the dynamical mean-field theory
(DMFT) can be achieved by mapping a correlated lattice model onto an impurity
model in which the impurity is coupled to an uncorrelated bath that consists of
a single site only. The two-site impurity model can be solved exactly. The
mapping is approximate. The self-consistency conditions are constructed in a
way that the resulting ``two-site DMFT'' reduces to the previously discussed
linearized DMFT for the Mott transition. It is demonstrated that a reasonable
description of the mean-field physics is possible with a minimum computational
effort. This qualifies the simple two-site DMFT for a systematic study of more
complex lattice models which cannot be treated by the full DMFT in a feasible
way. To show the strengths and limitations of the new approach, the single-band
Hubbard model is investigated in detail. The predictions of the two-site DMFT
are compared with results of the full DMFT. Internal consistency checks are
performed which concern the Luttinger sum rule, other Fermi-liquid relations
and thermodynamic consistency.Comment: LaTeX, 14 pages, 8 eps figures included, Phys. Rev. B (in press
Dynamical mean-field theory of indirect magnetic exchange
To analyze the physical properties arising from indirect magnetic exchange
between several magnetic adatoms and between complex magnetic nanostructures on
metallic surfaces, the real-space extension of dynamical mean-field theory
(R-DMFT) appears attractive as it can be applied to systems of almost arbitrary
geometry and complexity. While R-DMFT describes the Kondo effect of a single
adatom exactly, indirect magnetic (RKKY) exchange is taken into account on an
approximate level only. Here, we consider a simplified model system consisting
of two magnetic Hubbard sites ("adatoms") hybridizing with a non-interacting
tight-binding chain ("substrate surface"). This two-impurity Anderson model
incorporates the competition between the Kondo effect and indirect exchange but
is amenable to an exact numerical solution via the density-matrix
renormalization group (DMRG). The particle-hole symmetric model at half-filling
and zero temperature is used to benchmark R-DMFT results for the magnetic
coupling between the two adatoms and for the magnetic properties induced in the
substrate. In particular, the dependence of the local adatom and the nonlocal
adatom-adatom static susceptibilities as well as the magnetic response of the
substrate on the distance between the adatoms and on the strength of their
coupling with the substrate is studied. We find both, excellent agreement with
the DMRG data even on subtle details of the competition between RKKY exchange
and the Kondo effect but also complete failure of the R-DMFT, depending on the
parameter regime considered. R-DMFT calculations are performed using the
Lanczos method as impurity solver. With the real-space extension of the
two-site DMFT, we also benchmark a simplified R-DMFT variant.Comment: 14 pages, 8 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
Nonequilibrium sum rules for the retarded self-energy of strongly correlated electrons
We derive the first two moment sum rules of the conduction electron retarded
self-energy for both the Falicov-Kimball model and the Hubbard model coupled to
an external spatially uniform and time-dependent electric field (this
derivation also extends the known nonequilibrium moment sum rules for the
Green's functions to the third moment). These sum rules are used to further
test the accuracy of nonequilibrium solutions to the many-body problem; for
example, we illustrate how well the self-energy sum rules are satisfied for the
Falicov-Kimball model in infinite dimensions and placed in a uniform electric
field turned on at time t=0. In general, the self-energy sum rules are
satisfied to a significantly higher accuracy than the Green's functions sum
rules
Phase diagram of orbital-selective Mott transitions at finite temperatures
Mott transitions in the two-orbital Hubbard model with different bandwidths
are investigated at finite temperatures. By means of the self-energy functional
approach, we discuss the stability of the intermediate phase with one orbital
localized and the other itinerant, which is caused by the orbital-selective
Mott transition (OSMT). It is shown that the OSMT realizes two different
coexistence regions at finite temperatures in accordance with the recent
results of Liebsch. We further find that the particularly interesting behavior
emerges around the special condition and J=0, which includes a new type
of the coexistence region with three distinct states. By systematically
changing the Hund coupling, we establish the global phase diagram to elucidate
the key role played by the Hund coupling on the Mott transitions.Comment: 4 pages, 6 figure
Electron-correlation effects in appearance-potential spectra of Ni
Spin-resolved and temperature-dependent appearance-potential spectra of
ferromagnetic Nickel are measured and analyzed theoretically. The Lander
self-convolution model which relates the line shape to the unoccupied part of
the local density of states turns out to be insufficient. Electron correlations
and orbitally resolved transition-matrix elements are shown to be essential for
a quantitative agreement between experiment and theory.Comment: LaTeX, 6 pages, 2 eps figures included, Phys. Rev. B (in press
Proper weak-coupling approach to the periodic s-d(f) exchange model
The periodic s-d(f) exchange model is characterized by a wide variety of
interesting applications, a simple mathematical structure and a limited number
of reliable approximations which take care of the quantum nature of the
participating spins. We suggest the use of a projection-operator method for
getting information perturbationally, which are not accessible via diagrammatic
approaches. In this paper we present in particular results beyond perturbation
theory, which are obtained such that almost all exactly known limiting cases
are incorporated correctly. We discuss a variety of possible methods and
evaluate their consequences for one-particle properties. These considerations
serve as a guideline for a more effective approach to the model.Comment: 11 pages, 6 figures; accepted by Phys. Rev.
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