Compressing the two-particle Green's function using wavelets: Theory and application to the Hubbard atom

Abstract

Precise algorithms capable of providing controlled solutions in the presence of strong interactions are transforming the landscape of quantum many-body physics. Particularly exciting breakthroughs are enabling the computation of non-zero temperature correlation functions. However, computational challenges arise due to constraints in resources and memory limitations, especially in scenarios involving complex Green's functions and lattice effects. Leveraging the principles of signal processing and data compression, this paper explores the wavelet decomposition as a versatile and efficient method for obtaining compact and resource-efficient representations of the many-body theory of interacting systems. The effectiveness of the wavelet decomposition is illustrated through its application to the representation of generalized susceptibilities and self-energies in a prototypical interacting fermionic system, namely the Hubbard model at half-filling in its atomic limit. These results are the first proof-of-principle application of the wavelet compression within the realm of many-body physics and demonstrate the potential of this wavelet-based compression scheme for understanding the physics of correlated electron systems.

arXiv comment25 pages, 16 figures, 2 tables

References in corpus (41)

• Continuous-time Monte Carlo methods for quantum impurity models
• Quantum Cluster Theories
• Functional renormalization group approach to correlated fermion systems
• Diagrammatic routes to nonlocal correlations beyond dynamical mean field theory
• Observing gravitational-wave transient GW150914 with minimal assumptions
• Local Electronic Correlation at the Two-Particle Level
• Compressing Green's function using intermediate representation between imaginary-time and real-frequency domains
• w2dynamics: Local one- and two-particle quantities from dynamical mean field theory
• Non-existence of the Luttinger-Ward functional and misleading convergence of skeleton diagrammatic series for Hubbard-like models
• Fully Learnable Deep Wavelet Transform for Unsupervised Monitoring of High-Frequency Time Series
• Divergent Precursors of the Mott-Hubbard Transition at the Two-Particle Level
• Strong-Coupling Perturbation Theory of the Hubbard Model
• Breakdown of traditional many-body theories for correlated electrons
• Non-perturbative landscape of the Mott-Hubbard transition: Multiple divergence lines around the critical endpoint
• Divergences of the irreducible vertex functions in correlated metallic systems: Insights from the Anderson Impurity Model
• Unphysical and Physical Solutions in Many-Body Theories: from Weak to Strong Correlation
• Fingerprints of the local moment formation and its Kondo screening in the generalized susceptibilities of many-electron problems
• Attractive effect of a strong electronic repulsion -- the physics of vertex divergences
• Discrete Lehmann representation of imaginary time Green's functions
• Practical consequences of Luttinger-Ward functional multivaluedness for cluster DMFT methods
• Analytical investigation of singularities in two-particle irreducible vertex functions of the Hubbard atom
• Critical metal-insulator transition and divergence in a two-particle irreducible vertex in disordered and interacting electron systems
• Multipoint correlation functions: spectral representation and numerical evaluation
• Multiscale space-time ansatz for correlation functions of quantum systems based on quantics tensor trains
• Sparse Modeling in Quantum Many-Body Problems
• The Bethe-Salpeter equation at the critical end-point of the Mott transition
• Interplay between local response and vertex divergences in many-fermion systems with on-site attraction
• Overcomplete compact representation of two-particle Green's functions
• Performance analysis of a physically constructed orthogonal representation of imaginary-time Green's function
• libdlr: Efficient imaginary time calculations using the discrete Lehmann representation
• Sparse sampling and tensor network representation of two-particle Green's functions
• Efficient ab initio many-body calculations based on sparse modeling of Matsubara Green's function
• Solving the Bethe-Salpeter equation with exponential convergence
• Efficient ab initio Migdal-Eliashberg calculation considering the retardation effect in phonon-mediated superconductors
• Highly nonperturbative nature of the Mott metal-insulator transition: Two-particle vertex divergences in the coexistence region
• Non-perturbative intertwining between spin and charge correlations: A "smoking gun" single-boson-exchange result
• Fluctuations analysis of the spin susceptibility: Néel ordering revisited in dynamical mean field theory
• Sparse modeling of large-scale quantum impurity models with low symmetries
• Smooth self-energy in the exact-diagonalization-based dynamical mean-field theory: Intermediate-representation filtering approach
• Thermodynamic Stability at the Two-Particle Level
• Protection of Correlation-Induced Phase Instabilities by Exceptional Susceptibilities

Cited by in corpus (4)

• Two-particle calculations with quantics tensor trains: Solving the parquet equations
• Discrete Lehmann representation of three-point functions
• Entanglement across scales: Quantics tensor trains as a natural framework for renormalization
• Improvement of the simplification method for the local two-particle full-vertex towards precise frequency behavior