arXiv subjects

Hartmut Hafermann

Publications and source records attributed to Hartmut Hafermann.

At least 37 records · Page 2Linked to original sources

arXiv2018

Intersite electron correlations on inhomogeneous lattices: a real-space dual fermion approach

We develop a real-space extension of the dual fermion approach. This method is formulated in terms of real-space Green's functions and local vertex functions, which enables us to discuss local and nonlocal correlations in inhomogeneous systems with an arbitrary geometric structure. We first demonstrate that the approach gives us reasonable results for a homogenous periodic system by taking into account onsite and nearest-neighbor intersite correlations. Moreover, we study the half-filled Hubbard model on the quasiperiodic Penrose lattice and clarify the role of intersite correlations for the Mott transition. The intersite correlations lead to a rich structure in local observables which is inherited from the quasiperiodic structure of the lattice.

cond-mat.str-el↗

arXiv2017

Precursors of the insulating state in the square lattice Hubbard model

We study the two-dimensional square lattice Hubbard model for small to moderate interaction strengths $1\leq U/t\leq 4$ by means of the ladder dual fermion approach. The non-local correlations beyond dynamical mean-field theory lower the potential energy, lead to a maximum in the uniform susceptibility and induce a pseudogap in the density of states. While the self-energy exhibits precursors of a possible insulating phase linked to the appearance of long-range fluctuations, the metallic phase persists within the accessible temperature range. Finite-size effects affect results qualitatively. Upper bounds on the crossover temperature are found to be significantly lower than previously reported dynamical vertex approximation results at $U/t=1$.

cond-mat.str-el↗

arXiv2017

Polarization-Division Multiplexing Based on the Nonlinear Fourier Transform

Polarization-division multiplexed (PDM) transmission based on the nonlinear Fourier transform (NFT) is proposed for optical fiber communication. The NFT algorithms are generalized from the scalar nonlinear Schrödinger equation for one polarization to the Manakov system for two polarizations. The transmission performance of the PDM nonlinear frequency-division multiplexing (NFDM) and PDM orthogonal frequency-division multiplexing (OFDM) are determined. It is shown that the transmission performance in terms of Q-factor is approximately the same in PDM-NFDM and single polarization NFDM at twice the data rate and that the polarization-mode dispersion does not seriously degrade system performance. Compared with PDM-OFDM, PDM-NFDM achieves a Q-factor gain of 6.4 dB. The theory can be generalized to multi-mode fibers in the strong coupling regime, paving the way for the application of the NFT to address the nonlinear effects in space-division multiplexing.

cs.IT↗

arXiv2017

Diagrammatic Monte Carlo approach for diagrammatic extensions of dynamical mean-field theory -- convergence analysis of the dual fermion technique

The dual-fermion approach provides a formally exact prescription for calculating properties of a correlated electron system in terms of a diagrammatic expansion around dynamical mean-field theory (DMFT). Most practical implementations, however, neglect higher-order interaction vertices beyond two-particle scattering in the dual effective action and further truncate the diagrammatic expansion in the two-particle scattering vertex to a leading-order or ladder-type approximation. In this work we compute the dual-fermion expansion for the two-dimensional Hubbard model including all diagram topologies with two-particle interactions to high orders by means of a stochastic diagrammatic Monte Carlo algorithm. We benchmark the obtained self-energy against numerically exact Diagrammatic Determinant Monte Carlo simulations to systematically assess convergence of the dual-fermion series and the validity of these approximations. We observe that, from high temperatures down to the vicinity of the DMFT Néel transition, the dual-fermion series converges very quickly to the exact solution in the whole range of Hubbard interactions considered ($4 \leq U/t \leq 12$), implying that contributions from higher-order vertices are small. As the temperature is lowered further, we observe slower series convergence, convergence to incorrect solutions, and ultimately divergence. This happens in a regime where magnetic correlations become significant. We find however that the self-consistent particle-hole ladder approximation yields reasonable and often even highly accurate results in this regime.

cond-mat.str-el↗

arXiv2016

Design of MLSD-Based Receivers for Short-Range Optical Communications Using the Volterra Expansion

Maximum Likelihood Sequence Detectors (MLSD) have been largely used to mitigate the Chromatic Dispersion (CD) in Intensity Modulation/Direct Detection (IM/DD) optical communication systems. For practical applications, the high complexity of the receivers remains an important issue. In this paper, we analyze the design of MLSD-based receivers using the Orthogonal Volterra Kernel Model for IM/DD optical communication systems in Metro Optical applications. We discuss the impact in complexity and performance of the main parameters of the model and provide three design options for the MLSDbased receiver. Finally we provide numerical simulations showing the Bit Error Rate (BER) performances of the three considered designs for both On-Off Keying (OOK) and higher order Pulse Amplitude Modulation (PAM).

cs.IT↗

arXiv2016

Double occupancy in DMFT and the Dual Boson approach

We discuss the calculation of the double occupancy using Dynamical Mean-Field Theory (DMFT) in finite dimensions. The double occupancy can be determined from the susceptibility of the auxiliary impurity model or from the lattice susceptibility. The former method underestimates, whereas the latter overestimates the double occupancy. We illustrate this for the square-lattice Hubbard model. We propose an approach for which both methods lead to identical results by construction and which resolves this ambiguity. This self-consistent dual boson scheme results in a double occupancy that is numerically close to benchmarks available in the literature.

cond-mat.str-el↗

arXiv2016

Optical Fiber MIMO Channel Model and its Analysis

Technology is moving towards space division multiplexing in optical fiber to keep up the trend in rate increase over time and to avoid an imminent capacity crunch. Thus, it is of paramount interest to estimate the potential gains of this approach. As more spatial channels are being packed into a single fiber, the increased crosstalk necessitates the use of MIMO to guarantee reliable operation. In this paper, we exploit the analogy between an optical fiber and a model from mesoscopic physics - a chaotic cavity - to obtain a novel channel model for the optical fiber. The model captures both random distributed crosstalk and modedependent loss, which are described within the framework of scattering theory. Using tools from replica theory and random matrix theory, we derive the capacity of the fiber optical MIMO channel model.

cs.IT↗

arXiv2015

Intersite electron correlations in a Hubbard model on inhomogeneous lattices

We study intersite electron correlations in the half-filled Hubbard model on square lattices with periodic and open boundary conditions by means of a real-space dual fermion approach. By calculating renormalization factors, we clarify that nearest-neighbor intersite correlations already significantly reduce the critical interaction. The Mott transition occurs at U/t~6.4, where $U$ is the interaction strength and t is the hopping integral. This value is consistent with the quantum Monte Carlo results. This shows the importance of short-range intersite correlations, which are taken into account in the framework of the real-space dual fermion approach.

cond-mat.str-el↗

arXiv2015

Mechanisms of finite temperature magnetism in the three-dimensional Hubbard model

We examine the nature of the transition to the antiferromagnetically ordered state in the half-filled three-dimensional Hubbard model using the dual-fermion multiscale approach. Consistent with analytics, in the weak-coupling regime we find that spin-flip excitations across the Fermi surface are important, and that the strong coupling regime is described by Heisenberg physics. In the intermediate interaction, strong correlation regime we find aspects of both local and non-local correlations. We analyze the critical exponents of the transition in the strong coupling regime and find them to be consistent with Heisenberg physics down to an interaction of $U/t=10$.

cond-mat.str-el↗

arXiv2015

Thermodynamic consistency of the charge response in dynamical mean-field based approaches

We consider the thermodynamic consistency of the charge response function in the (extended) Hubbard model. In DMFT, thermodynamic consistency is preserved. We prove that the static, homogeneous DMFT susceptibility is consistent as long as vertex corrections obtained from the two-particle impurity correlation function are included. In presence of a nonlocal interaction, the problem may be treated within extended DMFT (EDMFT), or its diagrammatic extension, the dual boson approach. We show that here, maintaining thermodynamic consistency requires knowledge of three- and four-particle impurity correlation functions, which are typically neglected. Nevertheless, the dual boson approximation to the response is remarkably close to consistency. This holds even when two-particle vertex corrections are neglected. EDMFT is consistent only in the strongly correlated regime and near half-filling, where the physics is predominantly local.

cond-mat.str-el↗

arXiv2015

TRIQS: A Toolbox for Research on Interacting Quantum Systems

We present the TRIQS library, a Toolbox for Research on Interacting Quantum Systems. It is an open-source, computational physics library providing a framework for the quick development of applications in the field of many-body quantum physics, and in particular, strongly-correlated electronic systems. It supplies components to develop codes in a modern, concise and efficient way: e.g. Green's function containers, a generic Monte Carlo class, and simple interfaces to HDF5. TRIQS is a C++/Python library that can be used from either language. It is distributed under the GNU General Public License (GPLv3). State-of-the-art applications based on the library, such as modern quantum many-body solvers and interfaces between density-functional-theory codes and dynamical mean-field theory (DMFT) codes are distributed along with it.

cond-mat.str-el↗

arXiv2014

Beyond extended dynamical mean-field theory: Dual boson approach to the two-dimensional extended Hubbard model

The dual boson approach [Ann. Phys. 327, 1320 (2012)] provides a means to construct a diagrammatic expansion around the extended dynamical mean-field theory (EDMFT). In this paper, we present the numerical implementation of the approach and apply it to the extended Hubbard model with nearest-neighbor interaction $V$. We calculate the EDMFT phase diagram and study the effect of diagrams beyond EDMFT on the transition to the charge-ordered phase. Including diagrammatic corrections to the EDMFT polarization shifts the EDMFT phase boundary to lower values of $V$. The approach interpolates between the random phase approximation in the weak coupling limit and EDMFT for strong coupling. Neglecting vertex corrections leads to results reminiscent of the EDMFT+$GW$ approximation. We however find significant deviations from the dual boson results already for small values of the interaction, emphasizing the crucial importance of fermion-boson vertex corrections.

cond-mat.str-el↗

arXiv2014

Superconductivity, antiferromagnetism and phase separation in the two-dimensional Hubbard model: A dual-fermion approach

The dual-fermion approach offers a way to perform diagrammatic expansion around the dynamical mean-field theory. Using this formalism, the influence of antiferromagnetic fluctuations on the self-energy is taken into account through ladder-type diagrams in the particle-hole channel. The resulting phase diagram for the (quasi-)two-dimensional Hubbard model exhibits antiferromagnetism and d-wave superconductivity. Furthermore, a uniform charge instability, i.e., phase separation, is obtained in the low doping regime around the Mott insulator. We also examine spin/charge density wave fluctuations including d-wave symmetry. The model exhibits a tendency towards an unconventional charge density-wave, but no divergence of the susceptibility is found.

cond-mat.str-el↗

arXiv2014

Collective Charge Excitations of Strongly Correlated Electrons, Vertex Corrections and Gauge Invariance

We consider the collective, long-wavelength charge excitations in correlated media in presence of short- and long-range forces. As an example for the case of a short-range interaction, we examine the two-dimensional Hubbard model within dynamical mean-field theory (DMFT). It is shown explicitly that the DMFT susceptibility including vertex corrections respects the Ward identity and yields a manifestly gauge-invariant response in finite dimensions. For computing the susceptibility, we use a different expression and establish its formal equivalence to the standard DMFT formula. It allows for a more stable analytical continuation. We find a zero-sound mode expected for short-range forces. The relation between the vertex corrections, gauge invariance, and the appearance of the collective modes is discussed. Long-range forces are treated within extended dynamical mean-field theory. In order to obtain a gauge-invariant response, it is necessary to additionally incorporate some non local vertex corrections into the polarization. In doing so, we obtain plasmons in the three-dimensional Hubbard model. The plasma frequency is determined by the (single-particle) density distribution as a consequence of gauge invariance. We compare this result with the plasma frequency extracted from the analytical continuation of the susceptibility. It is in good agreement with the prediction from the gauge-invariance condition.

cond-mat.str-el↗

arXiv2014

From Hubbard bands to spin-polaron excitations in the doped Mott material Na$_x$CoO$_2$

We investigate the excitation spectrum of strongly correlated sodium cobaltate within a realistic many-body description beyond dynamical mean-field theory (DMFT). At lower doping around $x$=0.3, rather close to Mott-critical half-filling, the single-particle spectral function of Na$_x$CoO$_2$ displays an upper Hubbard band which is captured within DMFT. Momentum-dependent self-energy effects beyond DMFT become dominant at higher doping. Around a doping level of $x\sim 0.67$, the incoherent excitations give way to finite-energy spin-polaron excitations in close agreement with optics experiments. These excitations are a direct consequence of the formation of bound states between quasiparticles and paramagnons in the proximity to in-plane ferromagnetic ordering.

cond-mat.str-el↗

arXiv2014

Self-energy and vertex functions from hybridization expansion continuous-time quantum Monte Carlo for impurity models with retarded interaction

Optimized measurements for the susceptibility, self-energy, as well as three-leg and four-leg vertex functions are introduced for the continuous-time hybridization expansion quantum Monte Carlo solver for the impurity model in presence of a retarded interaction. The self-energy and vertex functions are computed from impurity averages which involve time integrals over the retarded interaction. They can be evaluated efficiently within the segment representation. These quantities are computed within dynamical mean-field theory in presence of plasmonic screening. In the antiadiabatic regime, the self-energy is strongly renormalized but retains features of the low energy scale set by the screened interaction. An explicit expression for its high-frequency behavior is provided. Across the screening-driven and interaction-driven metal-insulator transitions, the vertex functions are found to exhibit similar structural changes, which are hence identified as generic features of the Mott transition.

cond-mat.str-el↗

arXiv2014

Fermi Condensation Near van Hove Singularities Within the Hubbard Model on the Triangular Lattice

The proximity of the Fermi surface to van Hove singularities drastically enhances interaction effects and leads to essentially new physics. In this work we address the formation of flat bands ("Fermi condensation") within the Hubbard model on the triangular lattice and provide a detailed analysis from an analytical and numerical perspective. To describe the effect we consider both weak-coupling and strong-coupling approaches, namely the renormalization group and dual fermion methods. It is shown that the band flattening is driven by correlations and is well pronounced even at sufficiently high temperatures, of the order of 0.1-0.2 of the hopping parameter. The effect can therefore be probed in experiments with ultracold fermions in optical lattices.

cond-mat.str-el↗

arXiv2013

Efficient implementation of the continuous-time hybridization expansion quantum impurity solver

Strongly correlated quantum impurity problems appear in a wide variety of contexts ranging from nanoscience and surface physics to material science and the theory of strongly correlated lattice models, where they appear as auxiliary systems within dynamical mean-field theory. Accurate and unbiased solutions must usually be obtained numerically, and continuous-time quantum Monte Carlo algorithms, a family of algorithms based on the stochastic sampling of partition function expansions, perform well for such systems. With the present paper we provide an efficient and generic implementation of the hybridization expansion quantum impurity solver, based on the segment representation. We provide a complete implementation featuring most of the recently developed extensions and optimizations. Our implementation allows one to treat retarded interactions and provides generalized measurement routines based on improved estimators for the self-energy and for vertex functions. The solver is embedded in the ALPS-DMFT application package.

cond-mat.str-el↗