Truncated Unity Parquet Solver

Abstract

We present an implementation of a truncated unity parquet solver (TUPS) which solves the parquet equations using a truncated form-factor basis for the fermionic momenta. This way fluctuations from different scattering channels are treated on an equal footing. The essentially linear scaling of computational costs in the number of untruncated bosonic momenta allows us to treat system sizes of up to 76x76 discrete lattice momenta, unprecedented by previous unbiased methods that include the frequency dependence of the vertex. With TUPS, we provide the first numerical evidence that the parquet approximation might indeed respect the Mermin-Wagner theorem and further systematically analyze the convergence with respect to the number of form factors. Using a single form factor seems to qualitatively describe the physics of the half-filled Hubbard model correctly, including the pseudogap behaviour. Quantitatively, using a single or a few form factors only is not sufficient at lower temperatures or stronger coupling.

19 pages, 20 figures

References in corpus (47)

• The density-matrix renormalization group in the age of matrix product states
• A Common Thread: the pairing interaction for the unconventional superconductors
• Functional renormalization group approach to correlated fermion systems
• Stripe order in the underdoped region of the two-dimensional Hubbard model
• Competing electronic orders on Kagome lattices at van Hove filling
• Diagrammatic routes to nonlocal correlations beyond dynamical mean field theory
• Dynamical vertex approximation - a step beyond dynamical mean field theory
• Superconductivity and the Pseudogap in the two-dimensional Hubbard model
• 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
• Local Electronic Correlation at the Two-Particle Level
• 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
• w2dynamics: Local one- and two-particle quantities from dynamical mean field theory
• Comparing pertinent effects of antiferromagnetic fluctuations in the two and three dimensional Hubbard model
• From infinite to two dimensions through the functional renormalization group
• Efficient perturbation theory for quantum lattice models
• Critical properties of the half-filled Hubbard model in three dimensions
• Dynamical vertex approximation in its parquet implementation: application to Hubbard nano-rings
• Superconductivity, antiferromagnetism and phase separation in the two-dimensional Hubbard model: A dual-fermion approach
• Efficient implementation of the parquet equations -- role of the reducible vertex function and its kernel approximation
• Extended crossover from Fermi liquid to quasi-antiferromagnet in the half-filled 2D Hubbard model
• High-performance functional renormalization group calculations for interacting fermions
• Ab initio dynamical vertex approximation
• Multiloop functional renormalization group for general models
• Period 4 stripe in the extended two-dimensional Hubbard model
• Parquet approximation for the 4x4 Hubbard cluster
• Antiferromagnetic and d-wave pairing correlations in the strongly interacting two-dimensional Hubbard model from the functional renormalization group
• Pseudogap at hot spots in the two-dimensional Hubbard model at weak coupling
• Solving the Parquet Equations for the Hubbard Model beyond Weak Coupling
• Why the critical temperature of high-$T_{\mathrm{c}}$ cuprate superconductors is so low: The importance of the dynamical vertex structure
• Quantum criticality with a twist - interplay of correlations and Kohn anomalies in three dimensions
• Diagrammatic Monte Carlo approach for diagrammatic extensions of dynamical mean-field theory -- convergence analysis of the dual fermion technique
• Multiloop functional renormalization group for the two-dimensional Hubbard model: Loop convergence of the response functions
• Derivation of exact flow equations from the self-consistent parquet relations
• Dual parquet scheme for the two-dimensional Hubbard model: modelling low-energy physics of high-$T_c$ cuprates with high momentum resolution
• Models of the Pseudogap State of Two-Dimensional Systems
• Dynamical vertex approximation for the two-dimensional Hubbard model
• Anomalous self-energy and Fermi surface quasi-splitting in the vicinity of a ferromagnetic instability
• Thermodynamically consistent description of criticality in models of correlated electrons
• Dynamical vertex approximation for the attractive Hubbard model
• Quantum criticality in the two-dimensional periodic Anderson model
• Truncated-Unity Parquet Equations: Application to the Repulsive Hubbard Model
• Multiorbital effects in the functional renormalization group: A weak-coupling study of the Emery model
• Drude Weight of the Two-Dimensional Hubbard Model -- Reexamination of Finite-Size Effect in Exact Diagonalization Study --
• Competition between antiferromagnetic and charge density wave fluctuations in the extended Hubbard model
• Parquet dual fermion approach for the Falicov-Kimball model

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• Boson-Exchange Parquet Solver for dual fermions
• Multiscale space-time ansatz for correlation functions of quantum systems based on quantics tensor trains
• Fluctuation diagnostic of the nodal/antinodal dichotomy in the Hubbard model at weak coupling: a parquet dual fermion approach
• Self-consistent ladder D$\Gamma$A approach
• Tiling with triangles: parquet and $GW\gamma$ methods unified
• Reference results for the momentum space functional renormalization group
• How to read between the lines of electronic spectra: the diagnostics of fluctuations in strongly correlated electron systems
• Solving the Bethe-Salpeter equation with exponential convergence
• Pseudogap opening in the two-dimensional Hubbard model: A functional renormalization group analysis
• Parametrizations of local vertex corrections from weak to strong coupling: importance of the Hedin three-leg vertex
• Functional renormalization group for a large moiré unit cell
• Fulfillment of sum rules and Ward identities in the multiloop functional renormalization group solution of the Anderson impurity model
• TU${}^2$FRG -- a scalable approach for truncated unity functional renormalization group in generic fermionic models
• Electronic instabilities in Penrose quasi-crystals: competition, coexistence and collaboration of order
• Strongly correlated superconductivity with long-range spatial fluctuations
• Two-particle calculations with quantics tensor trains: Solving the parquet equations
• Real-frequency quantum field theory applied to the single-impurity Anderson model
• Data-driven compression of electron-phonon interactions
• Compactness of quantics tensor train representations of local imaginary-time propagators
• Consistency of potential energy in the dynamical vertex approximation
• Curie-Weiss susceptibility in strongly correlated electron systems
• Quasi-particle functional Renormalisation Group calculations in the two-dimensional half-filled Hubbard model at finite temperatures
• Subleading logarithmic behavior in the parquet formalism
• Parquet theory for molecular systems: Formalism and static kernel parquet approximation
• Single-boson exchange formulation of the Schwinger-Dyson equation and its application to the functional renormalization group
• Entanglement in the pseudogap regime of cuprate superconductors
• Intertwined fluctuations and isotope effects in the Hubbard-Holstein model on the square lattice from functional renormalization
• The finite-difference parquet method: Enhanced electron-paramagnon scattering opens a pseudogap
• Suppression of the charge fluctuations by nonlocal correlations close to the Mott transition
• 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
• Broadening and sharpening of the Drude peak through antiferromagnetic fluctuations
• Strong Boundary and Trap Potential Effects on Emergent Physics in Ultra-Cold Fermionic Gases
• A functional-analysis derivation of the parquet equation
• Compressing local vertex functions from the multipoint numerical renormalization group using quantics tensor cross interpolation
• Entanglement across scales: Quantics tensor trains as a natural framework for renormalization
• Diagrammatic bosonization, aspects of criticality, and the Hohenberg-Mermin-Wagner theorem in parquet approaches
• Functional renormalization with interaction flows: A single-boson exchange perspective and application to electron-phonon systems
• Surface Functional Renormalization Group for Layered Quantum Materials
• The plain and simple parquet approximation: single- and multi-boson exchange in the two-dimensional Hubbard model