arXiv subjects

Th. Maier

Publications and source records attributed to Th. Maier.

14 recordsLinked to original sources

arXiv2006

Multi-scale Extensions to Quantum Cluster Methods for Strongly Correlated Electron Systems

A numerically implementable Multi-scale Many-Body approach to strongly correlated electron systems is introduced. An extension to quantum cluster methods, it approximates correlations on any given length-scale commensurate with the strength of the correlations on the respective scale. Short length-scales are treated explicitly, long ones are addressed at a mean-field level and intermediate length-regime correlations are assumed to be weak and are approximated diagrammatically. To illustrate and test this method, we apply it to the one dimensional Hubbard model. The resulting multi-scale self-energy provides a very good quantitative agreement with substantially more numerically expensive, explicit Quantum Monte-Carlo calculations.

cond-mat.str-el↗

arXiv2006

Phase separation in the Hubbard model

Phase separation in the Hubbard model is investigated with the dynamical cluster approximation. We find that it is present in the paramagnetic solution for values of filling smaller than one and at finite temperature when a positive next-nearest neighbor hopping is considered. The phase separated region is characterized by a mixture of a strongly correlated metallic and Mott insulating phases. Our results indicate that phase separation is driven by the formation of doped regions with strong antiferromagnetic correlations and low kinetic energy

cond-mat.str-el↗

arXiv2006

Short-Range Ordered Phase of the Double-Exchange Model in Infinite Dimensions

Using dynamical mean-field theory, we have evaluated the magnetic instabilities and T=0 phase diagram of the double-exchange model on a Bethe lattice in infinite dimensions. In addition to ferromagnetic (FM) and antiferromagnetic (AF) phases, we also study a class of disordered phases with magnetic short-range order (SRO). In the weak-coupling limit, a SRO phase has a higher transition temperature than the AF phase for all fillings p below 1 and can even have a higher transition temperature than the FM phase. At T=0 and for small Hund's coupling J_H, a SRO state has lower energy than either the FM or AF phases for 0.26\le p < 1. Phase separation is absent in the J_H --> 0 limit but appears for any non-zero value of J_H.

cond-mat.str-el↗

arXiv2006

Magnetic Instabilities and Phase Diagram of the Double-Exchange Model in Infinite Dimensions

Dynamical mean-field theory is used to study the magnetic instabilities and phase diagram of the double-exchange (DE) model with Hund's coupling J_H >0 in infinite dimensions. In addition to ferromagnetic (FM) and antiferromagnetic (AF) phases, the DE model supports a broad class of short-range ordered (SRO) states with extensive entropy and short-range magnetic order. For any site on the Bethe lattice, the correlation parameter q of a SRO state is given by the average q= , where theta_i is the angle between any spin and its neighbors. Unlike the FM (q=0) and AF (q=1) transitions, the transition temperature of a SRO state (T_{SRO}) with 0 0 but appears for J_H\neq 0. For p near 1, PS occurs between an AF with p=1 and either a SRO or a FM phase. The stability of a SRO state at T=0 can be understood by examining the interacting DOS,which is gapped for any nonzero J_H in an AF but only when J_H exceeds a critical value in a SRO state.

cond-mat.mtrl-sci↗

arXiv2004

Physics of cuprates with the two-band Hubbard model - The validity of the one-band Hubbard model

We calculate the properties of the two-band Hubbard model using the Dynamical Cluster Approximation. The phase diagram resembles the generic phase diagram of the cuprates, showing a strong asymmetry with respect to electron and hole doped regimes, in agreement with experiment. Asymmetric features are also seen in one-particle spectral functions and in the charge, spin and d-wave pairing susceptibility functions. We address the possible reduction of the two-band model to a low-energy single-band one, as it was suggested by Zhang and Rice. Comparing the two-band Hubbard model properties with the single-band Hubbard model ones, we have found similar low-energy physics provided that the next-nearest-neighbor hopping term t' has a significant value ($t'/t \approx 0.3$). The parameter t' is the main culprit for the electron-hole asymmetry. However, a significant value of t' cannot be provided in a strict Zhang and Rice picture where the extra holes added into the system bind to the existing Cu holes forming local singlets. We notice that by considering approximate singlet states, such as plaquette ones, reasonable values of t', which capture qualitatively the physics of the two-band model can be obtained. We conclude that a single-band t-t'-U Hubbard model captures the basic physics of the cuprates concerning superconductivity, antiferromagnetism, pseudogap and electron-hole asymmetry, but is not suitable for a quantitative analysis or to describe physical properties involving energy scales larger than about 0.5 eV.

cond-mat.str-el↗

arXiv2004

Analytic continuation of QMC data with a sign problem

We present a Maximum Entropy method (MEM) for obtaining dynamical spectra from Quantum Monte Carlo data which have a sign problem. By relating the sign fluctuations to the norm of the spectra, our method properly treats the correlations between the measured quantities and the sign. The method greatly improves the quality and the resolution of the spectra, enabling it to produce good spectra even for poorly conditioned data where standard MEM fails.

cond-mat.stat-mech↗

arXiv2004

Quantum Cluster Theories

Quantum cluster approaches offer new perspectives to study the complexities of macroscopic correlated fermion systems. These approaches can be understood as generalized mean-field theories. Quantum cluster approaches are non-perturbative and are always in the thermodynamic limit. Their quality can be systematically improved, and they provide complementary information to finite size simulations. They have been studied intensively in recent years and are now well established. After a brief historical review, this article comparatively discusses the nature and advantages of these cluster techniques. Applications to common models of correlated electron systems are reviewed.

cond-mat.str-el↗

arXiv2001

A Quantum Monte Carlo algorithm for non-local corrections to the Dynamical Mean-Field Approximation

We present the algorithmic details of the dynamical cluster approximation (DCA), with a quantum Monte Carlo (QMC) method used to solve the effective cluster problem. The DCA is a fully-causal approach which systematically restores non-local correlations to the dynamical mean field approximation (DMFA) while preserving the lattice symmetries. The DCA becomes exact for an infinite cluster size, while reducing to the DMFA for a cluster size of unity. We present a generalization of the Hirsch-Fye QMC algorithm for the solution of the embedded cluster problem. We use the two-dimensional Hubbard model to illustrate the performance of the DCA technique. At half-filling, we show that the DCA drives the spurious finite-temperature antiferromagnetic transition found in the DMFA slowly towards zero temperature as the cluster size increases, in conformity with the Mermin-Wagner theorem. Moreover, we find that there is a finite temperature metal to insulator transition which persists into the weak-coupling regime. This suggests that the magnetism of the model is Heisenberg like for all non-zero interactions. Away from half-filling, we find that the sign problem that arises in QMC simulations is significantly less severe in the context of DCA. Hence, we were able to obtain good statistics for small clusters. For these clusters, the DCA results show evidence of non-Fermi liquid behavior and superconductivity near half-filling.

cond-mat.str-el↗

arXiv2000

Phase Diagram of the Hubbard Model: Beyond the Dynamical Mean Field

The Dynamical Cluster Approximation (DCA) is used to study non-local corrections to the dynamical mean field phase diagram of the two-dimensional Hubbard model. Regions of antiferromagnetic, d-wave superconducting, pseudo-gapped non-Fermi liquid, and Fermi liquid behaviors are found, in rough agreement with the generic phase diagram of the cuprates. The non-local fluctuations beyond the mean field both suppress the antiferromagnetism and mediate the superconductivity.

cond-mat.str-el↗

arXiv2000

d-wave Superconductivity in the Hubbard Model

The superconducting instabilities of the doped repulsive 2D Hubbard model are studied in the intermediate to strong coupling regime with help of the Dynamical Cluster Approximation (DCA). To solve the effective cluster problem we employ an extended Non Crossing Approximation (NCA), which allows for a transition to the broken symmetry state. At sufficiently low temperatures we find stable d-wave solutions with off-diagonal long range order. The maximal $T_c\approx 150K$ occurs for a doping $δ\approx 20%$ and the doping dependence of the transition temperatures agrees well with the generic high-$T_c$ phase diagram.

cond-mat.supr-con↗

arXiv1999

Pseudogaps in the 2D half-filled Hubbard model

We study the pseudogaps in the spectra of the half-filled 2D Hubbard model using both finite-size and dynamical cluster approximation (DCA) quantum Monte Carlo calculations. A charge pseudogap, accompanied by non-Fermi liquid behavior in the self energy, is shown to persist in the thermodynamic limit. The DCA (finite-size) method systematically underestimates (overestimates) the width of the pseudogap. A spin pseudogap is not seen at half-filling.

cond-mat.str-el↗

arXiv1999

A Non-Crossing Approximation for the Study of Intersite Correlations

We develop a Non-Crossing Approximation (NCA) for the effective cluster problem of the recently developed Dynamical Cluster Approximation (DCA). The DCA technique includes short-ranged correlations by mapping the lattice problem onto a self-consistently embedded periodic cluster of size $N_c$. It is a fully causal and systematic approximation to the full lattice problem, with corrections ${\cal{O}}(1/N_c)$ in two dimensions. The NCA we develop is a systematic approximation with corrections ${\cal{O}}(1/N_c^3)$. The method will be discussed in detail and results for the one-particle properties of the Hubbard model are shown. Near half filling, the spectra display pronounced features including a pseudogap and non-Fermi-liquid behavior due to short-ranged antiferromagnetic correlations.

cond-mat.str-el↗

arXiv1998

Electronic properties of the three-band Hubbard model

We study the electronic band-structure and transport properties of a CuO2-plane within the three-band Hubbard model. The Dynamical Mean-Field Theory (DMFT) is used to solve the many particle problem. The calculations show that the optical gap Delta_opt is given by excitations from the lower Hubbard band into the so called Zhang-Rice singlet band. The optical gap Delta_opt turns out to be considerably smaller than the charge transfer energy Delta (Delta=ep-ed) for a typical set of parameters, which is in agreement with experiment. For the two-dimensional CuO2-plane we investigated the dependency of the shape of the Fermi surface on the different hopping parameters t_CuO and t_OO. A value t_OO/t_CuO >0$ leads to a Fermi surface surrounding the M point. An additional different static shift of the oxygen energies is also considered to calculate the electronic response due to a displacement of the oxygen atoms given by a frozen phonon. The density-density correlation for the oxygen orbitals is linear in doping for both hole and electron doping but shows a different temperature dependency in the two regimes. In the first case it is temperature independent and increases upon doping, which leads to an increasing electron-phonon coupling for the B_1g-mode in high-Tc superconductors.

cond-mat.str-el↗

arXiv1998

Magnetic properties of the three-band Hubbard model

We present magnetic properties of the three-band Hubbard model in the para- and antiferromagnetic phase on a hypercubic lattice calculated with the Dynamical Mean-Field Theory (DMFT). To allow for solutions with broken spin-symmetry we extended the approach to lattices with AB-like structure. Above a critical sublattice magnetization m_d=0.5 one can observe rich structures in the spectral-functions similar to the t-J model which can be related to the well known bound states for one hole in the Neel-background. In addition to the one-particle properties we discuss the static spin-susceptiblity in the paramagnetic state at the points q=0 and q=(pi,pi,pi,...) for different dopings delta. The delta-T-phase-diagram exhibits an enhanced stability of the antiferromagnetic state for electron-doped systems in comparison to hole-doped. This asymmetry in the phase diagram is in qualitative agreement with experiments for high-T_c materials.

cond-mat.str-el↗