arXiv subjects

Erik G. C. P. van Loon

Publications and source records attributed to Erik G. C. P. van Loon.

31 records · Page 2Linked to original sources

arXiv2020

Second-order dual fermion for multi-orbital systems

In dynamical mean-field theory, the correlations between electrons are assumed to be purely local. The dual fermion approach provides a systematic way of adding non-local corrections to the dynamical mean-field theory starting point. Initial applications of this method were largely restricted to the single-orbital Hubbard model. Here, we present an implementation of second-order dual fermion for general multi-orbital systems and use this approach to investigate spatial correlations in SrVO$_3$. In addition, the approach is benchmarked in several exactly solvable small systems.

cond-mat.str-el↗

arXiv2020

The Bethe-Salpeter equation at the critical end-point of the Mott transition

Strong repulsive interactions between electrons can lead to a Mott metal-insulator transition. The Dynamical Mean-Field Theory (DMFT) explains the critical end-point and hysteresis region with single-particle concepts such as the spectral function and the quasiparticle weight. In this work, we reconsider the critical end point of the metal-insulator transition on the two-particle level. We show that the relevant eigenvalue and eigenvector of the non-local Bethe-Salpeter kernel provide a unified picture of the hysteresis region and of the critical end point of the Mott transition. In particular, they simultaneously explain the thermodynamics of the hysteresis region and the iterative stability of the DMFT equations. This analysis paves the way for a deeper understanding of phase transitions in correlated materials.

cond-mat.str-el↗

arXiv2019

Two-particle Fermi liquid parameters at the Mott transition: Vertex divergences, Landau parameters, and incoherent response in dynamical mean-field theory

We consider the interaction-driven Mott transition at zero temperature from the viewpoint of microscopic Fermi liquid theory. To this end, we derive an exact expression for the Landau parameters within the dynamical mean-field theory (DMFT) approximation to the single-band Hubbard model. At the Mott transition the symmetric and the anti-symmetric Landau parameter diverge. The vanishing compressibility at the Mott transition directly implies the divergence of the forward scattering amplitude in the charge sector, which connects the proximity of the Mott phase to a tendency towards phase separation. We verify the expected behavior of the Landau parameters in a DMFT application to the Hubbard model on the triangular lattice at finite temperature. Exact conservation laws and the Ward identity are crucial to capture vertex divergences related to the Mott transition. We furthermore generalize Leggett's formula for the static susceptibility of the Fermi liquid to the static fermion-boson response function. In the charge sector the limits of small transferred momentum and frequency of this response function commute at the Mott transition.

cond-mat.str-el↗

arXiv2019

Bandwidth renormalization due to the intersite Coulomb interaction

The theory of correlated electrons is currently moving beyond the paradigmatic Hubbard $U$, towards the investigation of intersite Coulomb interactions. Recent investigations have revealed that these interactions are relevant for the quantitative description of realistic materials. Physically, intersite interactions are responsible for two rather different effects: screening and bandwidth renormalization. We use a variational principle to disentangle the roles of these two processes and study how appropriate the recently proposed Fock treatment of intersite interactions is in correlated systems. The magnitude of this effect in graphene is calculated based on cRPA values of the intersite interaction. We also observe that the most interesting charge fluctuation phenomena actually occur at elevated temperatures, substantially higher than studied in previous investigations.

cond-mat.str-el↗

arXiv2018

Fermion-boson vertex within Dynamical Mean-Field Theory

In the study of strongly interacting systems, correlations on the two-particle level are receiving more and more attention. In this work, we study a particular two-particle correlation function: the fermion-boson vertex. It describes the response of the Green's function when an external field is applied and is an important ingredient of diagrammatic extensions of Dynamical Mean-Field Theory. We provide several perspectives on this object, using Ward identities, sum rules, perturbative analysis and asymptotic relations. We then use these tools to study the vertex across the doping-driven metal-insulator transition and find a divergence in the imaginary part.

cond-mat.str-el↗

arXiv2018

Second-order dual fermion approach to the Mott transition in the two-dimensional Hubbard model

We apply the dual fermion approach with a second-order approximation to the self-energy to the Mott transition in the two-dimensional Hubbard model. The approximation captures nonlocal dynamical short-range correlations as well as several features observed in studies using cluster dynamical mean-field theory. This includes a strong reduction of the critical interaction and inversion of the slope of the transition lines with respect to single-site dynamical mean-field theory. We show that these effects coincide with a much smaller momentum differentiation compared to cluster methods. We further discuss the role of the self-consistency condition and show that the approximation behaves as an asymptotic series at low temperature.

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↗

arXiv2016

A comparison between methods of analytical continuation for bosonic functions

In this article we perform a critical assessment of different known methods for the analytical continuation of bosonic functions, namely the maximum entropy method, the non-negative least-square method, the non-negative Tikhonov method, the Padé approximant method, and a stochastic sampling method. Three functions of different shape are investigated, corresponding to three physically relevant scenarios. They include a simple two-pole model function and two flavours of the non-interacting Hubbard model on a square lattice, i.e. a single-orbital metallic system and a two-orbitals insulating system. The effect of numerical noise in the input data on the analytical continuation is discussed in detail. Overall, the stochastic method by Mishchenko et al. [Phys. Rev. B \textbf{62}, 6317 (2000)] is shown to be the most reliable tool for input data whose numerical precision is not known. For high precision input data, this approach is slightly outperformed by the Padé approximant method, which combines a good resolution power with a good numerical stability. Although none of the methods retrieves all features in the spectra in the presence of noise, our analysis provides a useful guideline for obtaining reliable information of the spectral function in cases of practical interest.

cond-mat.str-el↗

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↗

arXiv2015

Ultralong-range order in the Fermi-Hubbard model with long-range interactions

We use the dual boson approach to reveal the phase diagram of the Fermi-Hubbard model with long-range dipole-dipole interactions. By using a large-scale finite-temperature calculation on a $64 \times 64$ square lattice we demonstrate the existence of a novel phase, possessing an `ultralong-range' order. The fingerprint of this phase -- the density correlation function -- features a non-trivial behavior on a scale of tens of the lattice sites. We study the properties and the stability of the ultralong-range ordered phase, and show that it is accessible in modern experiments with ultracold polar molecules and magnetic atoms.

cond-mat.quant-gas↗

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↗

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

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.

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