Functional renormalization group for fermion lattice models in three dimensions: application to the Hubbard model on the cubic lattice

Abstract

The channel-decomposed functional renormalization group (FRG) approach, most recently in the variant of truncated-unity-(TU-)FRG, has so far been used for various two-dimensional model systems. Yet, for many interesting material systems the third spatial dimension is of clear relevance. Therefore FRG schemes working in three spatial dimensions (3D) are definitely on the wishlist. Here we demonstrate that a 3D TUFRG scheme can be set up in straightforward extension of previous 2D codes and gives physically sensible results with affordable numerical effort, both regarding the qualitative as well as the quantitative description. The computed phase diagram of the three-dimensional Hubbard model at half filling or perfect nesting shows a phase transition to a \((π,π,π)\)-ordered antiferromagnetic ground state for repulsive interactions at an energy scale that compares well with other numerical approaches in the literature. Furthermore, the method allowed us to detect a \(d\)-wave pairing and a concurring \((π,π,0)\) antiferromagnetic ground state in the hole doped Hubbard model.

arXiv comment8 pages, 9 figures

References in corpus (25)

• Functional renormalization group approach to correlated fermion systems
• Competing electronic orders on Kagome lattices at van Hove filling
• Functional renormalization group and variational Monte Carlo studies of the electronic instabilities in graphene near 1/4 doping
• Functional Renormalization Group for multi-orbital Fermi Surface Instabilities
• Efficient Parametrization of the Vertex Function, $\Omega$-Scheme, and the (t,t')-Hubbard Model at Van Hove Filling
• Phase diagram of the three-dimensional Hubbard model at half filling
• Critical properties of the half-filled Hubbard model in three dimensions
• Critical temperature and the transition from quantum to classical order parameter fluctuations in the three-dimensional Heisenberg antiferromagnet
• High-frequency asymptotics of the vertex function: diagrammatic parametrization and algorithmic implementation
• High-performance functional renormalization group calculations for interacting fermions
• Multiloop functional renormalization group that sums up all parquet diagrams
• Néel temperature and thermodynamics of the half-filled 3D Hubbard model by Diagrammatic Determinant Monte Carlo
• Efficient calculation of the antiferromagnetic phase diagram of the 3D Hubbard model
• Mechanisms of finite temperature magnetism in the three-dimensional Hubbard model
• Frequency Dependent Vertex Functions of the (t,t')-Hubbard Model at Weak Coupling
• Magnetic phase diagram of the Hubbard model
• Non-separable frequency dependence of two-particle vertex in interacting fermion systems
• Multiloop functional renormalization group for the two-dimensional Hubbard model: Loop convergence of the response functions
• Spectral properties of the three-dimensional Hubbard model
• Competing electronic instabilities of extended Hubbard models on the honeycomb lattice: A functional Renormalization Group calculation with high wavevector resolution
• Pseudogap opening in the two-dimensional Hubbard model: A functional renormalization group analysis
• Self-energy effects in functional renormalization group flows of the two-dimensional $t$-$t^{\prime }$ Hubbard model away from van Hove filling
• Truncated unity functional renormalization group for multiband systems with spin-orbit coupling
• Fermionic functional renormalization group for first-order phase transitions: a mean-field model
• Symmetry breaking in the Hubbard model at weak coupling

Cited by in corpus (14)

• TU${}^2$FRG -- a scalable approach for truncated unity functional renormalization group in generic fermionic models
• divERGe implements various Exact Renormalization Group examples
• Phase transitions in partial summation methods: Results from the 3D Hubbard model
• Itinerant magnetism of chromium under pressure: a DFT+DMFT study
• Competition between d-wave superconductivity and magnetism in uniaxially strained Sr2RuO4
• Magnetic phase diagram of the three-dimensional doped Hubbard model
• Consistent combination of truncated-unity functional renormalization group and mean-field theory
• Quantum spin Hall insulator on the honeycomb lattice induced by ferromagnetic exchange interaction
• Spin susceptibilities in magnetic type-I and type-II Weyl semimetals
• Functional renormalization group for extremely correlated electrons
• Bad Metal Behavior and Lifshitz Transition of a Nagaoka Ferromagnet
• Variational Diagrammatic Monte-Carlo Built on Dynamical Mean-Field Theory
• Spin bond order driven by extended repulsive interactions in doped graphene
• Surface Functional Renormalization Group for Layered Quantum Materials