Maximum Entropy Analytic Continuation for Spectral Functions with Non-Positive Spectral Weight

Abstract

Information about the pairing mechanism for superconductivity is contained in the spectral weight for the anomalous (Gorkov) Green function. In the most general case, this spectral weight can change sign on the positive real axis or even be complex in the presence of broken time-reversal symmetry. This renders impossible the direct analytic continuation with Maximum Entropy methods of numerical results obtained for the anomalous Green function either in Matsubara frequency or in imaginary time. Here we show that one can define auxiliary Green functions that allow one to extract the anomalous spectral weight in the most general multi-orbital spin-singlet or triplet cases with no particular symmetry. As a simple example, we treat the case of lead in Eliashberg theory: Maximum Entropy analytic continuation with auxiliary Green functions (MaxEntAux) allows us to recover spectral functions that change sign on the positive real axis. The approach can be extended to transport quantities.

References in corpus (4)

• A Common Thread: the pairing interaction for the unconventional superconductors
• Resilience of d-wave superconductivity to nearest-neighbor repulsion
• Pairing Glue in the Two Dimensional Hubbard Model
• Quasiparticle Properties of the Superconducting State of the Two Dimensional Hubbard Model

Cited by in corpus (27)

• Algorithms for optimized maximum entropy and diagnostic tools for analytic continuation
• Maximum entropy formalism for the analytic continuation of matrix-valued Green's functions
• Sparse modeling approach to analytical continuation of imaginary-time quantum Monte Carlo data
• Analytical Continuation of Matrix-Valued Functions: Carathéodory Formalism
• The Average Spectrum Method for Analytic Continuation: Efficient Blocked Modes Sampling and Dependence on Discretization Grid
• Maximum Quantum Entropy Method
• Antagonistic effects of nearest-neighbor repulsion on the superconducting pairing dynamics in the doped Mott insulator regime
• Extending the average spectrum method: Grid points sampling and density averaging
• SpM: Sparse modeling tool for analytic continuation of imaginary-time Green's function
• Unconventional Pairing from Local Orbital Fluctuations in Strongly Correlated A${}_3$C${}_{60}$
• Learned Optimizers for Analytic Continuation
• Minimal Pole Representation and Controlled Analytic Continuation of Matsubara Response Functions
• Maximum entropy analytic continuation for frequency-dependent transport coefficients with non-positive spectral weight
• Minimal pole representation and analytic continuation of matrix-valued correlation functions
• Noise Enhanced Neural Networks for Analytic Continuation
• Superconductivity enhanced by pair fluctuations between wide and narrow bands
• Stochastic pole expansion method
• Numerical approaches for calculating the low-field dc Hall coefficient of the doped Hubbard model
• Pairing enhanced by local orbital fluctuations in a model for monolayer FeSe
• Maximum entropy analytic continuation of anomalous self-energies
• Superconductivity in the two-dimensional Hubbard model with cellular dynamical mean-field theory: a quantum impurity model analysis
• TRIQS/Nevanlinna: Implementation of the Nevanlinna Analytic Continuation method for noise-free data
• Barycentric rational function approximation made simple: A fast analytic continuation method for Matsubara Green's functions
• Intrinsic Thermal Hall Effect in Mott Insulators
• Nevanlinna Analytic Continuation for Migdal-Eliashberg Theory
• Dynamics of superconducting pairs in the two-dimensional Hubbard model
• Many-body electronic structure, self-doped double-exchange, and Hund metallicity in 1T-CrTe2 bulk and monolayer