TU${}^2$FRG -- a scalable approach for truncated unity functional renormalization group in generic fermionic models

Abstract

Describing the emergence of phases of condensed matter is one of the central challenges in physics. For this purpose many numerical and analytical methods have been developed, each with their own strengths and limitations. The functional renormalization group is one of these methods bridging between efficiency and accuracy. In this paper we derive a new truncated unity (TU) approach unifying real- and momentum space TU, called TU${}^2$FRG. This formalism significantly improves the scaling compared to conventional momentum (TU)FRG when applied to large unit-cell models and models where the translational symmetry is broken.

arXiv comment9 pages, 4 figures

References in corpus (50)

• Magic-angle graphene superlattices: a new platform for unconventional superconductivity
• The density-matrix renormalization group in the age of matrix product states
• Many body localization and thermalization in quantum statistical mechanics
• Metal-insulator transition in a weakly interacting many-electron system with localized single-particle states
• Observation of many-body localization of interacting fermions in a quasi-random optical lattice
• The many-body localization phase transition
• Massive Dirac fermions in a ferromagnetic kagome metal
• Exploring the many-body localization transition in two dimensions
• Functional renormalization group approach to correlated fermion systems
• On Many-Body Localization for Quantum Spin Chains
• Moiré heterostructures as a condensed matter quantum simulator
• Superconductivity in rhombohedral trilayer graphene
• Isospin magnetism and spin-triplet superconductivity in Bernal bilayer graphene
• Half and quarter metals in rhombohedral trilayer graphene
• Efficient Parametrization of the Vertex Function, $\Omega$-Scheme, and the (t,t')-Hubbard Model at Van Hove Filling
• Tracking the Footprints of Spin Fluctuations: A MultiMethod, MultiMessenger Study of the Two-Dimensional Hubbard Model
• The temperature-flow renormalization group and the competition between superconductivity and ferromagnetism
• Spin Fluctuation-Induced Superconductivity in Organic Compounds
• High-temperature topological superconductivity in twisted double layer copper oxides
• Magnetic and superconducting instabilities of the Hubbard model at the van Hove filling
• High-frequency asymptotics of the vertex function: diagrammatic parametrization and algorithmic implementation
• High-performance functional renormalization group calculations for interacting fermions
• Nature of Many-Body Localization and Transitions by Density Matrix Renormaliztion Group and Exact Diagonalization Studies
• Multiloop functional renormalization group for general models
• Interaction flow method for many-fermion systems
• Spin-fluctuation exchange study of superconductivity in two- and three-dimensional single-band Hubbard models
• Truncated Unity Parquet Solver
• Frequency Dependent Vertex Functions of the (t,t')-Hubbard Model at Weak Coupling
• Quantitative functional renormalization-group description of the two-dimensional 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
• Spin-fluctuation-induced pairing in twisted bilayer graphene
• Competing electronic instabilities of extended Hubbard models on the honeycomb lattice: A functional Renormalization Group calculation with high wavevector resolution
• Reference results for the momentum space functional renormalization group
• Single boson exchange representation of the functional renormalization group for strongly interacting many-electron systems
• Inherited and flatband-induced ordering in twisted graphene bilayers
• Dynamical correlations in multiorbital Hubbard models: Fluctuation-exchange approximations
• Functional renormalization group for a large moiré unit cell
• Functional Renormalization Group Approach for Inhomogeneous Interacting Fermi-Systems
• Antiferromagnetism and competing charge instabilities of electrons in strained graphene from Coulomb interactions
• Electronic instabilities in Penrose quasi-crystals: competition, coexistence and collaboration of order
• Detecting phases in one-dimensional many-fermion systems with the functional renormalization group
• Functional renormalization group for fermion lattice models in three dimensions: application to the Hubbard model on the cubic lattice
• Orbital-dependent self-energy effects and consequences for the superconducting gap structure in multi-orbital correlated electron systems
• Competing electronic orders on a heavily doped honeycomb lattice with enhanced exchange coupling
• Functional Renormalization Group Approach for Inhomogeneous One-Dimensional Fermi Systems with Finite-Ranged Interactions
• Many-body localization and the area law in two dimensions
• Effect of exchange interaction on electronic instabilities in the honeycomb lattice: A functional renormalization group study
• Approximating the frequency dependence of the effective interaction in the functional renormalization group for many-fermion systems
• Strong Boundary and Trap Potential Effects on Emergent Physics in Ultra-Cold Fermionic Gases

Cited by in corpus (19)

• Altermagnetic phase transition in a Lieb metal
• The kagome Hubbard model from a functional renormalization group perspective
• divERGe implements various Exact Renormalization Group examples
• Theory of intervalley-coherent AFM order and topological superconductivity in tWSe${}_2$
• Superconductivity of repulsive spinless fermions with sublattice potentials
• Spin and pair density waves in 2D altermagnetic metals
• Competition between d-wave superconductivity and magnetism in uniaxially strained Sr2RuO4
• Better Integrators for Functional Renormalization Group Calculations
• Magic angle of Sr${}_2$RuO${}_4$: Optimizing correlation-driven superconductivity
• 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
• Addressing energy density functionals in the language of path-integrals II: Comparative study of functional renormalization group techniques applied to the (0+0)-D $O(N)$-symmetric ${\phi }^4$-theory
• Functional renormalization group for extremely correlated electrons
• Kekulé order from diffuse nesting near higher-order Van Hove points
• Functional renormalization with interaction flows: A single-boson exchange perspective and application to electron-phonon systems
• Surface Functional Renormalization Group for Layered Quantum Materials
• Theory of unconventional magnetism in a Cu-based kagome metal
• Many-body correlations in Floquet steady-states: Frequency-resolved renormalization group of the driven Anderson impurity
• Spin bond order driven by extended repulsive interactions in doped graphene