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Benchmark data for "Reference results for the momentum space functional renormalization group"

Jacob Beyer, Jonas B. Hauck, Lennart Klebl

Published Jan 14, 2022• 1 citation
Publisher

Abstract

This repository contains the reference data for the paper "Reference results for the momentum space functional renormalization group". We encourage all readers to compare their results to ours.
DOI
10.5281/zenodo.5848605

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In this thesis a novel computational approach for functional Renormalization Group (fRG) investigations regarding interacting fermions on two-dimensional lattices is derived. The approach is based on the exchange-parametrization fRG [C. Husemann and M. Salmhofer. Phys. Rev. B, 79:195125.] concerning the two-fermion interaction, with additional insertions of truncated partitions of unity that are inspired by the singular-mode fRG [W.-S. Wang, Y.-Y. Xiang, Q.-H. Wang, et al.. Phys. Rev. B, 85:035414.]. These insertions decouple the fermionic propagators from the exchange propagators and thereby lead to a separation of the underlying equations. It is argued that this separation is numerically advantageous and may pave the way for refined, large-scale computational fRG investigations. Furthermore, on the basis of speedup data gained from an implementation of the novel scheme, it is shown that the new equation structure facilitates efficient calculations on a large number of multi-core CPUs. Utilizing the methodical development, two applications are presented afterwards: Firstly, the scheme is applied to the t-t' Hubbard model on a square lattice. In order to test the method, the convergence of the results with respect to increasing truncation length of the partition of unity is analyzed and a comparison to findings from previous fRG studies is drawn. The test yields a fast convergence in most parts of the investigated parameter range. Moreover, it was found that the older findings are approximately reproduced using a short truncation length, while quantitative corrections to the previous results are obtained using longer truncation lengths. In addition to these method focused investigations, the high momentum-space resolution of the implementation was utilized to study ordering vectors of antiferromagnetic phases. A comparison to calculations solely based on the magnetic channel revealed that the inter-channel feedback, as contained in the fRG, generates support for commensurate antiferromagnetic orderings. The second application addresses a modified version of the previous model, in which a Coulomb-like long-range interaction term is added to the local Hubbard interaction. In this work a solution is presented on how the long-range interaction can be implemented in a momentum-space fRG scheme without encountering singularities. Afterwards, phase diagrams are given that compare the results of calculations using short- and long-ranged interactions, showing significantly lower critical scales in the long-range scenario. Finally, screening lengths are extracted from the fRG outcome and are compared to those calculated in a 'random phase approximation'. The comparison reveals quantitative differences between both values. However, the results indicate that the charge screening is not changed qualitatively by the feedback from other channels, i.e., at van Hove filling the screening length tends to zero in both cases.
The ability of entanglement renormalization (ER) to generate a proper real-space renormalization group (RG) flow in extended quantum systems is analyzed in the setting of harmonic lattice systems in D =1 and 2 spatial dimensions. A conceptual overview of the steps involved in momentum-space RG is provided and contrasted against the equivalent steps in the real-space setting. The real-space RG flow, as generated by ER, is compared against the exact results from momentum-space RG, including an investigation of a critical fixed point and the effect of relevant and irrelevant perturbations.