Low-energy effective interactions beyond the constrained random-phase approximation by the functional renormalization group

In the derivation of low-energy effective models for solids targeting the bands near the Fermi level, the constrained random phase approximation (cRPA) has become an appreciated tool to compute the effective interactions. The Wick-ordered constrained functional renormalization group (cfRG) generalizes the cRPA approach by including all interaction channels in an unbiased way. Here we present applications of the cfRG to two simple multi-band systems and compare the resulting effective interactions to the cRPA. First we consider a multiband model for monolayer graphene, where we integrate out the $\sigma$-bands to get an effective theory for $\pi$-bands. It turns out that terms beyond cRPA are strongly suppressed by the different $xy$-plane reflection symmetry of the bands. In our model the cfRG-corrections to cRPA become visible when one disturbs this symmetry difference slightly, however without qualitative changes. This study shows that the embedding or layering of two-dimensional electronic systems can alter the effective interaction parameters beyond what is expected from screening considerations. The second example is a one-dimensional model for a diatomic system reminiscent of a CuO chain, where we consider an effective theory for Cu 3d-like orbitals. Here the fRG data shows relevant and qualitative corrections compared to the cRPA results. We argue that the new interaction terms affect the magnetic properties of the low-energy model.Comment: 17 pages, 14 figure

Two-particle-correlations in a functional renormalization group scheme using a dynamical mean-field theory approach

We apply a recently introduced hybridization-flow functional renormalization group scheme for Anderson-like impurity models as an impurity solver in a dynamical mean-field theory (DMFT) approach to lattice Hubbard models. We present how this scheme is capable of reproducing metallic and insulating solutions of the lattice model. Our setup also offers a numerically rather inexpensive method to calculate two-particle correlation functions. For the paramagnetic Hubbard-model on the Bethe lattice in infinite dimensions we calculate the local two-particle-vertex for the metallic and the insulating phase. Then we go to a two-site cluster-DMFT-scheme for the two-dimensional Hubbard-model that includes short-range antiferromagnetic fluctuations and obtain the local and non-local two-particle-vertex-functions. We discuss the rich frequency structures of these vertices and compare with the vertex in the single-site solution.Comment: 22 pages, 15 figure

An alternative functional renormalization group approach to the single impurity Anderson model

We present an alternative functional renormalization group (fRG) approach to the single-impurity Anderson model at finite temperatures. Starting with the exact self-energy and interaction vertex of a small system ('core') containing a correlated site, we switch on the hybridization with a non-interacting bath in the fRG-flow and calculate spectra of the correlated site. Different truncations of the RG-flow-equations and choices of the core are compared and discussed. Furthermore we calculate the linear conductance and the magnetic susceptibility as functions of temperature and interaction strength. The signatures of Kondo physics arising in the flow are compared with numerical renormalization group results.Comment: 16 page

Effective low-energy Hamiltonians for interacting nanostructures

We present a functional renormalization group (fRG) treatment of trigonal graphene nanodiscs and composites thereof, modeled by finite-size Hubbard-like Hamiltonians with honeycomb lattice structure. At half filling, the noninteracting spectrum of these structures contains a certain number of half-filled states at the Fermi level. For the case of trigonal nanodiscs, including interactions between these degenerate states was argued to lead to a large ground state spin with potential spintronics applications. Here we perform a systematic fRG flow where the excited single-particle states are integrated out with a decreasing energy cutoff, yielding a renormalized low-energy Hamiltonian for the zero-energy states that includes effects of the excited levels. The numerical implementation corroborates the results obtained with a simpler Hartree-Fock treatment of the interaction effects within the zero-energy states only. In particular, for trigonal nanodiscs the degeneracy of the one-particle-states with zero-energy turns out to be very robust against influences of the higher levels. As an explanation, we give a general argument that within this fRG scheme the zero-energy degeneracy remains unsplit under quite general conditions and for any size of the trigonal nanodisc. We furthermore discuss the differences in the effective Hamiltonian and their ground states of single nanodiscs and composite bow-tie-shaped systems.Comment: 13 page

Tumor Suppressor Function of Syk in Human MCF10A In Vitro and Normal Mouse Mammary Epithelium In Vivo

The normal function of Syk in epithelium of the developing or adult breast is not known, however, Syk suppresses tumor growth, invasion, and metastasis in breast cancer cells. Here, we demonstrate that in the mouse mammary gland, loss of one Syk allele profoundly increases proliferation and ductal branching and invasion of epithelial cells through the mammary fat pad during puberty. Mammary carcinomas develop by one year. Syk also suppresses proliferation and invasion in vitro. siRNA or shRNA knockdown of Syk in MCF10A breast epithelial cells dramatically increased proliferation, anchorage independent growth, cellular motility, and invasion, with formation of functional, extracellular matrix-degrading invadopodia. Morphological and gene microarray analysis following Syk knockdown revealed a loss of luminal and differentiated epithelial features with epithelial to mesenchymal transition and a gain in invadopodial cell surface markers CD44, CD49F, and MMP14. These results support the role of Syk in limiting proliferation and invasion of epithelial cells during normal morphogenesis, and emphasize the critical role of Syk as a tumor suppressor for breast cancer. The question of breast cancer risk following systemic anti-Syk therapy is raised since only partial loss of Syk was sufficient to induce mammary carcinomas

Drug-target identification in COVID-19 disease mechanisms using computational systems biology approaches

Introduction: The COVID-19 Disease Map project is a large-scale community effort uniting 277 scientists from 130 Institutions around the globe. We use high-quality, mechanistic content describing SARS-CoV-2-host interactions and develop interoperable bioinformatic pipelines for novel target identification and drug repurposing. Methods: Extensive community work allowed an impressive step forward in building interfaces between Systems Biology tools and platforms. Our framework can link biomolecules from omics data analysis and computational modelling to dysregulated pathways in a cell-, tissue- or patient-specific manner. Drug repurposing using text mining and AI-assisted analysis identified potential drugs, chemicals and microRNAs that could target the identified key factors. Results: Results revealed drugs already tested for anti-COVID-19 efficacy, providing a mechanistic context for their mode of action, and drugs already in clinical trials for treating other diseases, never tested against COVID-19. Discussion: The key advance is that the proposed framework is versatile and expandable, offering a significant upgrade in the arsenal for virus-host interactions and other complex pathologies.Peer Reviewe

Drug-target identification in COVID-19 disease mechanisms using computational systems biology approaches

IntroductionThe COVID-19 Disease Map project is a large-scale community effort uniting 277 scientists from 130 Institutions around the globe. We use high-quality, mechanistic content describing SARS-CoV-2-host interactions and develop interoperable bioinformatic pipelines for novel target identification and drug repurposing. MethodsExtensive community work allowed an impressive step forward in building interfaces between Systems Biology tools and platforms. Our framework can link biomolecules from omics data analysis and computational modelling to dysregulated pathways in a cell-, tissue- or patient-specific manner. Drug repurposing using text mining and AI-assisted analysis identified potential drugs, chemicals and microRNAs that could target the identified key factors.ResultsResults revealed drugs already tested for anti-COVID-19 efficacy, providing a mechanistic context for their mode of action, and drugs already in clinical trials for treating other diseases, never tested against COVID-19. DiscussionThe key advance is that the proposed framework is versatile and expandable, offering a significant upgrade in the arsenal for virus-host interactions and other complex pathologies

Single impurity Anderson model and dynamical mean field theory : a functional renormalization group study

An essential role for the description of correlated quantum many-particle systems is played by impurity problems. These consist of a small number of localized orbitals, where the electrons are subject to a Coulomb-interaction, coupled to noninteracting bath degrees of freedom. Impurity models are used for the description of magnetic impurities in metals, of quantum points in nanostructures, and in the context of the dynamical mean field theory (DMFT). For their solution a large number of numerical methods exists. We mention here quantum Monte Carlo methods, the numerical renormalization group, or the exact diagonalization method. In this thesis we introduce a new approach to impurity problems, which is based on the functional renormalization group (fRG). In contrast to the methods mentioned above this approach is approximative, but it can be applied with comparatively lower numerical effort. The aim of this thesis is to examine the advantages and limits of this method. An important role in this connection is played by the single impurity Anderson model (SIAM), which is already understood very well with other methods and is seen as a prototype for models with strong local correlations. The spin fluctuations of this model are governed by the so-called Kondo energy scale and a central question of this thesis is whether this scale can be reproduced with our approach. We begin with a short introduction to the Green's function formalism for correlated quantum many particle systems. Then the fRG flow equations for the one-particle irreducible vertex functions are deduced, and several approximation schemes are discussed. In chapter 4 we introduce the fRG scheme used in this thesis. At first the SIAM is mapped to a semi-infinite chain, in which the interacting orbital is given by the first site of this chain. The system is then subdivided into two parts. The first part, which is called 'core', consists of the interacting orbital and the first L bath sites. The remaining bath sites form the second part. At the beginning both parts are decoupled from each other such that the core can be solved exactly. Starting with this exact solution the coupling between the core and the remaining bath sites is switched on slowly in a renormalization group flow. This way it is possible to calculate the one-particle and two-particle correlation functions on the correlated site. We call this flow scheme 'hybridization flow'. The flow equations are formulated in an effective theory on the first bath site outside the core, which turns out to be advantageous compared to other implementations of the hybridization flow. In chapter 5 this hybridization flow method is applied to the SIAM with semi-elliptic bath density of states. We discuss the differences which arise for different core-sizes (L = 0,1,2,3) and for different truncations of the fRG flow equations. In the cases L=0 and L=2 the local Fermi liquid properties of the SIAM and the associated Kondo scale can not be reproduced in both approximation schemes. For the core sizes L=1 and L=3 the ground state of the core is already a spin singlet state in the beginning of the flow and the Fermi liquid properties are reproduced. The Kondo energy scale, which determines the width of the central quasi-particle peak and the size of the local spin-susceptibility, is however not accurately resolved. This is partly due to the finite temperature used in our implementation such that for larger interaction strength the temperature is above the Kondo energy scale. The application of the hybridization flow method to quantum impurity problems in the context of the DMFT is discussed in chapter 6. In this approach lattice models with a local interaction, like the Hubbard model, are mapped to an effective impurity problem for a single lattice site embedded in a dynamical mean field representing the influence of the other electrons. This scheme is exact in infinitely many dimensions and a nonperturbative approximation method for finite-dimensional systems. In particular the Mott metal-insulator transition in the Hubbard model is successfully described by this method. One class of quantities, which is easily accessible from the hybridization flow scheme, is given by the local two-particle correlation functions. These play an essential role in non-local extensions of the DMFT. Therefore we mainly focus on these quantities. At first we apply our flow scheme to the Hubbard model on the Bethe lattice in infinite dimensions and calculate the local one-particle irreducible vertex functions in the insulating and the metallic phase in good agreement with previous calculations, which use the exact diagonalization method as impurity solver. After this we extend our flow scheme to a cluster DMFT method, which includes short-range antiferromagnetic correlations and calculate again the local and non-local vertex functions for the two-dimensional Hubbard model. We compare these to the results of the single-site DMFT

Racial disparities in prostate cancer: A complex interplay between socioeconomic inequities and genomics.

The largest US cancer health disparity exists in prostate cancer, with Black men having more than a two-fold increased risk of dying from prostate cancer compared to all other races. This disparity is a result of a complex network of factors including socioeconomic status (SES), environmental exposures, and genetics/biology. Inequity in the US healthcare system has emerged as a major driver of disparity in prostate cancer outcomes and has raised concerns that the actual incidence rates may be higher than current estimates. However, emerging studies argue that equalizing healthcare access will not fully eliminate racial health disparities and highlight the important role of biology. Significant differences have been observed in prostate cancer biology between ancestral groups that may contribute to prostate cancer health disparities. Notably, relative to White men, Black men with prostate cancer exhibit increased androgen receptor signaling, genomic instability, metabolic dysregulation, and inflammatory and cytokine signaling. Immediate actions are needed to increase multi-center, interdisciplinary research to bridge the gap between social and biological determinants of prostate cancer health disparities