arXiv subjects

Michael Potthoff

Publications and source records attributed to Michael Potthoff.

67 records · Page 4Linked to original sources

arXiv2010

Variational cluster approach to ferromagnetism in infinite dimensions and in one-dimensional chains

The variational cluster approach (VCA) is applied to study spontaneous ferromagnetism in the Hubbard model at zero temperature. We discuss several technical improvements of the numerical implementation of the VCA which become necessary for studies of a ferromagnetically ordered phase, e.g. more accurate techniques to evaluate the variational ground-state energy, improved local as well as global algorithms to find stationary points, and different methods to locate the magnetic phase transition. Using the single-site VCA, i.e. the dynamical impurity approximation (DIA), the ferromagnetic phase diagram of the model in infinite dimensions is worked out. The results are compared with previous dynamical mean-field studies for benchmarking purposes. The DIA results provide a unified picture of ferromagnetism in the infinite-dimensional model by interlinking different parameter regimes that are governed by different mechanisms for ferromagnetic order. Using the DIA and the VCA, we then study ferromagnetism in one-dimensional Hubbard chains with nearest and next-nearest-neighbor hopping t2. In comparison with previous results from the density-matrix renormalization group, the phase diagram is mapped out as a function of the Hubbard-U, the electron filling and t2. The stability of the ferromagnetic ground state against local and short-range non-local quantum fluctuations is discussed.

cond-mat.str-el↗

arXiv2010

Importance of local correlations for the order parameter of high-Tc superconductors

It is shown that local temporal correlations in addition to non-local spatial correlations are important to understand the size and the doping dependence of the d-wave superconducting order parameter of high-temperature superconductors. To this end, the hole- and electron-doped two-dimensional Hubbard model at zero temperature is considered and treated by an extension of the variational cluster approximation. Within this approach, the effects of temporal correlations can be studied systematically and in a thermodynamically consistent way by comparing results obtained from different reference clusters. Contact can be made with previous cellular (plaquette) dynamical mean-field calculations. This shows that temporal correlations considerably decrease the order parameter and provide a substantial gain of binding energy. Besides, a few methodical insights regarding real-space quantum-cluster approaches are obtained in addition.

cond-mat.str-el↗

arXiv2009

Accessing thermodynamics from dynamical cluster-embedding approaches

Dynamical quantum-cluster approaches, such as different cluster extensions of the dynamical mean-field theory (cluster DMFT) or the variational cluster approximation (VCA), combined with efficient cluster solvers, such as the quantum Monte-Carlo (QMC) method, provide controlled approximations of the single-particle Green's function for lattice models of strongly correlated electrons. To access the thermodynamics, however, a thermodynamical potential is needed. We present an efficient numerical algorithm to compute the grand potential within cluster-embedding approaches that are based on novel continuous-time QMC schemes: It is shown that the numerically exact cluster grand potential can be obtained from a quantum Wang-Landau technique to reweight the coefficients in the expansion of the partition function. The lattice contributions to the grand potential are computed by a proper infinite summation over Matsubara frequencies. A proof of principle is given by applying the VCA to antiferromagnetic (short-range) order in the two-dimensional Hubbard model at finite temperatures.

cond-mat.str-el↗

arXiv2008

First order Mott transition at zero temperature in two dimensions: Variational plaquette study

The nature of the metal-insulator Mott transition at zero temperature has been discussed for a number of years. Whether it occurs through a quantum critical point or through a first order transition is expected to profoundly influence the nature of the finite temperature phase diagram. In this paper, we study the zero temperature Mott transition in the two-dimensional Hubbard model on the square lattice with the variational cluster approximation. This takes into account the influence of antiferromagnetic short-range correlations. By contrast to single-site dynamical mean-field theory, the transition turns out to be first order even at zero temperature.

cond-mat.str-el↗

arXiv2007

Mott transition in one dimension: Benchmarking dynamical cluster approaches

The variational cluster approach (VCA) is applied to the one-dimensional Hubbard model at zero temperature using clusters (chains) of up to ten sites with full diagonalization and the Lanczos method as cluster solver. Within the framework of the self-energy-functional theory (SFT), different cluster reference systems with and without bath degrees of freedom, in different topologies and with different sets of variational parameters are considered. Static and one-particle dynamical quantities are calculated for half-filling as a function of U as well as for fixed U as a function of the chemical potential to study the interaction- and filling-dependent metal-insulator (Mott) transition. The recently developed Q-matrix technique is used to compute the SFT grand potential. For benchmarking purposes we compare the VCA results with exact results available from the Bethe ansatz, with essentially exact dynamical DMRG data, with (cellular) dynamical mean-field theory and full diagonalization of isolated Hubbard chains. Several issues are discussed including convergence of the results with cluster size, the ability of cluster approaches to access the critical regime of the Mott transition, efficiency in the optimization of correlated-site vs. bath-site parameters and of multi-dimensional parameter optimization. We also study the role of bath sites for the description of excitation properties and as charge reservoirs for the description of filling dependencies. The VCA turns out to be a computationally cheap method which is competitive with established cluster approaches.

cond-mat.str-el↗

arXiv2007

Non-perturbative conserving approximations and Luttinger's sum rule

Weak-coupling conserving approximations can be constructed by truncations of the Luttinger-Ward functional and are well known as thermodynamically consistent approaches which respect macroscopic conservation laws as well as certain sum rules at zero temperature. These properties can also be shown for variational approximations that are generated within the framework of the self-energy-functional theory without a truncation of the diagram series. Luttinger's sum rule represents an exception. We analyze the conditions under which the sum rule holds within a non-perturbative conserving approximation. Numerical examples are given for a simple but non-trivial dynamical two-site approximation. The validity of the sum rule for finite Hubbard clusters and the consequences for cluster extensions of the dynamical mean-field theory are discussed.

cond-mat.str-el↗

arXiv2007

Self-energy-functional theory for systems of interacting electrons with disorder

Based on a functional-integral formalism, a generalization of the self-energy-functional theory (SFT) is proposed which is applicable to systems of interacting electrons with disorder. Similar to the pure case without disorder, a variational principle is set up which gives the physical (disorder) self-energy as a stationary point of the (averaged) grand potential. Although the resulting self-energy functional turns out to be more complicated, the formal structure of the theory can be retained since the unknown part of the functional is universal. This allows to construct non-perturbative and thermodynamically consistent approximations via searching for a stationary point on a restricted domain of the functional. The theory and the possible approximations are worked out for models with local interactions and local disorder. This results in a derivation of different mean-field approaches and various cluster extensions, including well-known concepts as the statistical dynamical mean-field theory, the molecular coherent-potential approximation and the dynamical cluster approximation. Due to the common formal framework provided by the SFT, one achieves a general systematization of dynamical approaches, i.e. approaches based on the spectrum of one-particle excitations. New mean-field and new cluster schemes naturally appear in this framework and complement the existing ones. Their prospects for future applications are discussed.

cond-mat.str-el↗

arXiv2005

Systematics of approximations constructed from dynamical variational principles

The systematics of different approximations within the self-energy-functional theory (SFT) is discussed for fermionic lattice models with local interactions. In the context of the SFT, an approximation is essentially given by specifying a reference system with the same interaction but a modified non-interacting part of the Hamiltonian which leads to a partial decoupling of degrees of freedom. The reference system defines a space of trial self-energies on which an optimization of the grand potential as a functional of the self-energy Omega[Sigma] is performed. As a stationary point is not a minimum in general and does not provide a bound for the exact grand potential, however, it is {\em a priori} unclear how to judge on the relative quality of two different approximations. By analyzing the Euler equation of the SFT variational principle, it is shown that a stationary point of the functional on a subspace given by a reference system composed of decoupled subsystems is also a stationary point in case of the coupled reference system. On this basis a strategy is suggested which generates a sequence of systematically improving approximations. The discussion is actually relevant for any variational approach that is not based on wave functions and the Rayleigh-Ritz principle.

cond-mat.str-el↗

arXiv2005

Correlated band structure and the ground-state phase diagram in high-Tc cuprates

We review results obtained with a recently proposed variational cluster approach (VCA) for the competition between d-wave superconductivity (dSC) and antiferromagnetism (AF) in the high-Tc cuprates. Comparing the single-particle spectra of a two-dimensional Hubbard model with quantum Monte-Carlo (QMC) and experimental data, we verify that the VCA correctly treats the low-energy excitations. The cluster calculations reproduce the overall ground-state phase diagram of the high-temperature superconductors both for electron- and hole-doping. In particular, they include salient features such as the enhanced robustness of the AF state in case of electron doping. For electron- but also for hole-doping, we clearly identify a tendency to phase separation into a mixed AF-dSC phase at low and a pure dSC-phase at high doping.

cond-mat.supr-con↗

arXiv2005

Dynamical variational principles for strongly correlated electron systems

The self-energy-functional approach (SFA) is discussed in the context of different variational principles for strongly correlated electron systems. Formal analogies between static and dynamical variational approaches, different types of approximation strategies and the relations to density-functional and dynamical mean-field theory are emphasized. The discussion elucidates the strengths of the SFA in the construction of new non-perturbative approximations but also the limitations of the approach and thereby opens up future perspectives.

cond-mat.str-el↗

arXiv2004

Non-perturbative construction of the Luttinger-Ward functional

For a system of correlated electrons, the Luttinger-Ward functional provides a link between static thermodynamic quantities on the one hand and single-particle excitations on the other. The functional is useful to derive several general properties of the system as well as for the formulation of thermodynamically consistent approximations. Its original construction, however, is perturbative as it is based on the weak-coupling skeleton-diagram expansion. Here, it is shown that the Luttinger-Ward functional can be derived within a general functional-integral approach. This alternative and non-perturbative approach stresses the fact that the Luttinger-Ward functional is universal for a large class of models.

cond-mat.str-el↗

arXiv2004

Disorder- and correlation-driven metal-insulator transitions

Metal-insulator transitions driven by disorder (Delta) and/or by electron correlations (U) are investigated within the Anderson-Hubbard model with local binary-alloy disorder using a simple but consistent mean-field approach. The Delta-U phase diagram is derived and discussed for T=0 and finite temperatures.

cond-mat.str-el↗

arXiv2003

Self-energy-functional approach to systems of correlated electrons

The grand potential of a system of interacting electrons is considered as a stationary point of a self-energy functional. It is shown that a rigorous evaluation of the functional is possible for self-energies that are representable within a certain reference system. The variational scheme allows to construct new non-perturbative and thermodynamically consistent approximations. Numerical results illustrate the practicability of the method.

cond-mat.str-el↗