Competing order in correlated electron systems made simple: Consistent fusion of functional renormalization and mean-field theory

Abstract

We derive an efficient and unbiased method for computing order parameters in correlated electron systems with competing instabilities. Charge, magnetic and pairing fluctuations above the energy scale of spontaneous symmetry breaking are taken into account by a functional renormalization group flow, while the formation of order below that scale is treated in mean-field theory. The method captures fluctuation driven instabilities such as $d$-wave superconductivity. As a first application we study the competition between antiferromagnetism and superconductivity in the ground state of the two-dimensional Hubbard model.

5 pages, 2 figures

References in corpus (10)

• Exact evolution equation for the effective potential
• Functional Renormalization Group for multi-orbital Fermi Surface Instabilities
• Competition between d-wave superconductivity and antiferromagnetism in the 2D Hubbard model
• A finite-frequency functional RG approach to the single impurity Anderson model
• Renormalized mean-field analysis of antiferromagnetism and d-wave superconductivity in the two-dimensional Hubbard model
• Renormalization group flow for fermionic superfluids at zero temperature
• Superconductivity in the attractive Hubbard model: functional renormalization group analysis
• Nodal quasiparticles and the onset of spin density wave order in the cuprates
• Spin-density-wave order in cuprates
• Parametrization of Nambu vertex in a singlet superconductor

Cited by in corpus (47)

• The nonperturbative functional renormalization group and its applications
• The Hubbard model: A computational perspective
• Coexistence of incommensurate magnetism and superconductivity in the two-dimensional Hubbard model
• Characterization of quantum spin liquids and their spinon band structures via functional renormalization
• Fermionic two-loop functional renormalization group for correlated fermions: Method and application to the attractive Hubbard model
• Dimerization tendencies of the pyrochlore Heisenberg antiferromagnet: A functional renormalization group perspective
• Single boson exchange representation of the functional renormalization group for strongly interacting many-electron systems
• Dynamical functional renormalization group computation of order parameters and critical temperatures in the two-dimensional Hubbard model
• Comprehensive mean-field analysis of magnetic and charge orders in the two-dimensional Hubbard model
• Theory of the Evolution of Superconductivity in Sr${}_2$RuO${}_4$ under Anisotropic Strain
• SU(2) gauge theory of the pseudogap phase in the two-dimensional Hubbard model
• Altermagnetic phase transition in a Lieb metal
• Functional renormalization group study of orbital fluctuation mediated superconductivity: Impact of the electron-boson coupling vertex corrections
• Self-energy effects in functional renormalization group flows of the two-dimensional $t$-$t^{\prime }$ Hubbard model away from van Hove filling
• Role of four-fermion interaction and impurity in the states of two-dimensional semi-Dirac materials
• Scaling relations and multicritical phenomena from Functional Renormalization
• Partial bosonisation for the two-dimensional Hubbard model: How well does it work?
• Accessing the ordered phase of correlated Fermi systems: vertex bosonization and mean-field theory within the functional renormalization group
• Competing electronic orders on a heavily doped honeycomb lattice with enhanced exchange coupling
• Functional renormalization group study of an eight-band model for the iron arsenides
• Functional renormalization group for commensurate antiferromagnets: Beyond the mean-field picture
• Theory of intervalley-coherent AFM order and topological superconductivity in tWSe${}_2$
• Single-boson exchange functional renormalization group application to the two-dimensional Hubbard model at weak coupling
• Phase stiffness in an antiferromagnetic superconductor
• Competition between d-wave superconductivity and magnetism in uniaxially strained Sr2RuO4
• Functional renormalization and mean-field approach to multiband systems with spin-orbit coupling: Application to the Rashba model with attractive interaction
• Impact of ordering competition on the global phase diagram of iron pnictides
• Fermion-fermion interaction driven instability and criticality of quadratic band crossing systems with the breaking of time-reversal symmetry
• Renormalization group analysis of competition between distinct order parameters
• Interaction-driven first-order and higher-order topological superconductivity
• Space of non-Fermi liquids
• Quantum criticality of fermion velocities and critical temperature nearby a putative quantum phase transition in the $d$-wave superconductors
• Low-Energy Effective Theory at a Quantum Critical Point of the Two-Dimensional Hubbard Model: Mean-Field Analysis
• Quantum spin Hall insulator on the honeycomb lattice induced by ferromagnetic exchange interaction
• Fermion-fermion interaction driven phase transitions in rhombohedral trilayer graphene
• Consistent combination of truncated-unity functional renormalization group and mean-field theory
• Spin-fluctuation glue disfavors high-critical temperature of superconductivity?
• Critical behavior around the fixed points driven by fermion-fermion interactions and disorders in the nodal-line superconductors
• Strong Boundary and Trap Potential Effects on Emergent Physics in Ultra-Cold Fermionic Gases
• Anomaly of longitudinal spin susceptibility at superconducting instability inside a magnetic phase
• Kohn-Luttinger-like mechanism for unconventional charge density waves
• Kekulé order from diffuse nesting near higher-order Van Hove points
• Spin susceptibility in a pseudogap state with fluctuating spiral magnetic order
• Nesting instability of gapless U(1) spin liquids with spinon Fermi pockets in two dimensions
• Beyond on-site Hubbard interaction in charge dynamics of cuprate superconductors
• Spin bond order driven by extended repulsive interactions in doped graphene
• Competing instabilities of the extended Hubbard model on the triangular lattice: Truncated-unity functional renormalization group and application to moiré materials