Functional renormalization group for extremely correlated electrons

Abstract

At strong on-site repulsion $U$, the fermionic Hubbard model realizes an extremely correlated electron system. In this regime, it is natural to derive the low-energy physics with the help of non-canonical operators acting on a projected Hilbert space without double occupancies. Using a strong-coupling functional renormalization group technique, we study the physics of such extreme correlations in the strict $U=\infty$ limit, where only kinematic interactions due to the Hilbert space projection remain. For nearest-neighbor hopping on a square lattice, we find that the electronic spectrum is significantly renormalized, with bandwidth and quasi-particle residue strongly decreasing with increasing electron density. On the other hand, damping and particle-hole asymmetry increase, while a polaronic continuum forms in the hole sector, below the single-particle band. Fermi liquid phenomenology applies only at low densities, where the system remains paramagnetic. At higher densities, we find a bad metal with strong magnetic correlations, indicating that the ground state is the Nagaoka ferromagnet at high densities and a stripe antiferromagnet at intermediate densities. Both in the paramagnetic and the ferromagnetic regimes, we observe a violation of Luttinger's theorem.

30 pages, 25 figures

References in corpus (73)

• Exact evolution equation for the effective potential
• Aspects of the Functional Renormalisation Group
• Functional renormalization group approach to correlated fermion systems
• The nonperturbative functional renormalization group and its applications
• Computational Studies of Quantum Spin Systems
• Diagrammatic routes to nonlocal correlations beyond dynamical mean field theory
• Observation of Spatial Charge and Spin Correlations in the 2D Fermi-Hubbard Model
• How bad metals turn good: spectroscopic signatures of resilient quasiparticles
• Efficient Parametrization of the Vertex Function, $\Omega$-Scheme, and the (t,t')-Hubbard Model at Van Hove Filling
• Fate of the false Mott-Hubbard transition in two dimensions
• Tracking the Footprints of Spin Fluctuations: A MultiMethod, MultiMessenger Study of the Two-Dimensional Hubbard Model
• On the fulfillment of Ward identities in the functional renormalization group approach
• Diagrammatic Monte Carlo
• Non-existence of the Luttinger-Ward functional and misleading convergence of skeleton diagrammatic series for Hubbard-like models
• Protected nodes and the collapse of the Fermi arcs in high Tc cuprates
• From infinite to two dimensions through the functional renormalization group
• Controlling Feynman diagrammatic expansions: physical nature of the pseudo gap in the two-dimensional Hubbard model
• On the Reconstructed Fermi Surface in the Underdoped Cuprates
• Topological Lifshitz transitions
• Nagaoka ferromagnetism observed in a quantum dot plaquette
• Renormalization group flows into phases with broken symmetry
• High-performance functional renormalization group calculations for interacting fermions
• Extended crossover from Fermi liquid to quasi-antiferromagnet in the half-filled 2D Hubbard model
• A Fermi-Hubbard Optical Tweezer Array
• Impact of nonlocal correlations over different energy scales: A Dynamical Vertex Approximation study
• Phases of the infinite U Hubbard model
• First-Matsubara-frequency rule in a Fermi liquid. Part I: Fermionic self-energy
• Antiferromagnetic and d-wave pairing correlations in the strongly interacting two-dimensional Hubbard model from the functional renormalization group
• Analytic continuation by averaging Padé approximants
• Observation of Nagaoka Polarons in a Fermi-Hubbard Quantum Simulator
• Frequency Dependent Vertex Functions of the (t,t')-Hubbard Model at Weak Coupling
• Spin and charge correlations across the metal-to-insulator crossover in the half-filled $2d$ Hubbard model
• Quantitative functional renormalization-group description of the two-dimensional Hubbard model
• Non-separable frequency dependence of two-particle vertex in interacting fermion systems
• Directly imaging spin polarons in a kinetically frustrated Hubbard system
• Ferromagnetism in the Hubbard model: A constructive approach
• Pseudogaps in the t-J model: Extended DMFT study
• Hidden Fermi Liquid: The Secret of High Tc Cuprates
• Topological interpretation of Luttinger theorem
• Hidden Fermi Liquid: Self-Consistent Theory for the Normal State of High-Tc Superconductors
• A dynamical mean-field theory study of Nagaoka ferromagnetism
• Two-dimensional t-J model at moderate doping
• Origin and fate of the pseudogap in the doped Hubbard model
• The itinerant ferromagnetic phase of the Hubbard model
• Extremely correlated Fermi liquid theory meets Dynamical mean-field theory: Analytical insights into the doping-driven Mott transition
• Breakdown of Landau Theory in Overdoped Cuprates near the Onset of Superconductivity
• Canonical representation for electrons and its application to the Hubbard model
• Extremely Correlated Fermi Liquids: The Formalism
• TU${}^2$FRG -- a scalable approach for truncated unity functional renormalization group in generic fermionic models
• Efficient vertex parametrization for the constrained functional renormalization group for effective low-energy interactions in multiband systems
• Transport Anomalies of the Strange Metal: Resolution by Hidden Fermi Liquid Theory
• Extremely Correlated Quantum Liquids
• Luttinger sum rule for finite systems of correlated electrons
• Functional renormalization group for fermion lattice models in three dimensions: application to the Hubbard model on the cubic lattice
• Zero-magnon sound in quantum Heisenberg ferromagnets
• Polaronic mechanism of Nagaoka ferromagnetism in Hubbard models
• A generating functional approach to the Hubbard model
• Effective approach to the Nagaoka regime of the two dimensional t-J model
• Influence of Magnetism and Correlation on the Spectral Properties of Doped Mott Insulators
• The foot, the fan, and the cuprate phase diagram: Fermi-volume-changing quantum phase transitions
• Strong-coupling diagrammatic Monte Carlo technique for correlated fermions and frustrated spins
• Breakdown of the Nagaoka phase at finite doping
• Linked-cluster expansion for the Green's function of the infinite-U Hubbard model
• Extremely correlated fermi liquid of $t$-$J$ model in two dimensions
• Diagrammatic $\lambda$ series for extremely correlated Fermi liquids
• Electronic spectral properties of the two-dimensional infinite-U Hubbard model
• Magnetic phase diagram of the infinite-U Hubbard model with nearest- and next nearest-neighbor hoppings
• The splitting of electrons and violation of the Luttinger sum rule
• Finite-Temperature Kinetic Ferromagnetism in the Square Lattice Hubbard Model
• Instability of Nagaoka State and Quantum Phase Transition via Kinetic Frustration Control
• Ferromagnetism vs. Antiferromagnetism in Narrow-Band Systems: Competition Between Quantum Geometry and Band Dispersion
• The finite-difference parquet method: Enhanced electron-paramagnon scattering opens a pseudogap
• Functional renormalization group without functional integrals: implementing Hilbert space projections for strongly correlated electrons via Hubbard X-operators

Cited by in corpus (1)

• Bad Metal Behavior and Lifshitz Transition of a Nagaoka Ferromagnet