Source-linked AI summary
adapol: Adaptive pole-fitting for quantum many-body physics
Zhen Huang, Chia-Nan Yeh, Lin Lin, Nils Wentzell, Jason Kaye, Hugo U. R. Strand
TL;DR
Pole fitting is a crucial step in several numerical methods, but adoption of existing methods has been limited by a lack of widely deployed, user-friendly software. adapol provides a simple, self-contained package for these fits, and prior work reports more compact approximations than generic DLR for a fixed Green’s function.
Problem
Pole fitting is a crucial step in several numerical methods, while a lack of widely deployed, user-friendly software has limited adoption of existing methods.
Source: Statement of Need · pp. 1–2Method
adapol implements an AAA-based pole-fitting approach and provides a self-contained interface for fitting Matsubara data or compressing existing pole expansions.
Source: State of the field · p. 2, Software design · p. 2Results
Prior work showed that adapol consistently yields a more compact pole approximation than generic DLR for a fixed, given Green’s function.
Source: Research impact statement · p. 2Takeaways & Limitations
The package offers documented, configurable fitting and compression functions, examples, and a TRIQS interface for codes requiring Matsubara pole fitting.
Source: Software design · p. 2
Abstract
from arXiv · showhide
We describe adapol, a Python package for fitting Matsubara Green's functions, self-energies, and hybridization functions by a compact sum of simple poles with real pole locations and matrix-valued residues. This pole-fitting step arises in many contexts, including hybridization fitting for quantum impurity solvers based on exact diagonalization, perturbation theory, and tensor networks, the compression of existing pole expansions such as the discrete Lehmann representation, diagrammatic methods based on discrete pole representations, and the analytic continuation of Matsubara Green's functions. adapol uses a modified version of the AAA rational approximation algorithm to estimate pole locations, and non-convex optimization to refine them. This procedure yields accurate and compact fits in a black-box and noise-robust manner. adapol provides a simple, self-contained interface with extensive documentation and examples, as well as an interface to the TRIQS package.
Statement of Need
Pole fitting is a crucial step in several numerical methods, and self-consistent applications need black-box fitting with controlled accuracy. adapol addresses a lack of widely deployed, user-friendly software with a simple, self-contained interface.
Statement of Need
- Pole fitting is a crucial step across these numerical methods.The cited applications include quantum impurity solvers based on exact diagonalization.Source: Statement of Need · pp. 1–2
- Pole fitting is used in hybridization fitting for impurity solvers, perturbation theory, tensor-network time evolution, analytic continuation, and diagrammatic methods.In self-consistent applications such as dynamical mean-field theory, the fitting step needs a black-box algorithm with controlled accuracy.Source: Statement of Need · pp. 1–2
- A lack of widely deployed, user-friendly software has limited adoption of pole-fitting methods, leaving practitioners with ad-hoc optimization or Padé approximants.adapol addresses this gap with a simple, self-contained interface and few user parameters.Source: Statement of Need · p. 2
State of the field
The field has pursued Prony-based methods and AAA rational approximation followed by non-convex optimization. adapol and MiniPole implement these distinct approaches, making them available for comparison.
State of the field
- Recent pole-fitting methods follow two approaches: Prony’s method and its variants, or AAA rational approximation followed by non-convex optimization.The passage cites Ying (2022a, 2022b), Zhang et al. (2024), Zhang & Gull (2024), and Nakatsukasa et al. (2018) for these approaches.Source: State of the field · p. 2
- MiniPole implements the Prony-based approach, while adapol implements the AAA-based approach described in Huang et al. (2023, 2025).The passage identifies these as distinct methods.Source: State of the field · p. 2
- The availability of both packages will allow users to compare the two approaches.Source: State of the field · p. 2
Software design
adapol accepts Matsubara data or an existing pole expansion and offers configurable fitting, documentation, examples, and a TRIQS interface.
Software design
- Users can fit Matsubara data or compress an existing pole expansion, such as a discrete Lehmann representation.Source: Software design · p. 2
- Users can choose whether to optimize the AAA result and specify either a maximum pole count or a target error tolerance.Source: Software design · p. 2
- The package provides extensive API documentation, example notebooks, and an interface to TRIQS.Source: Software design · p. 2
Research impact statement
Compact pole approximations matter in applications where computational costs grow with approximation size. Prior work reports that adapol gives a more compact approximation than generic DLR for a fixed Green’s function.
Research impact statement
- Computational costs often scale exponentially with pole count, making compact approximations important in exact-diagonalization impurity solvers and diagrammatic evaluation.Tensor-network quantum impurity solvers also benefit substantially from compact hybridization-function approximations.Source: Research impact statement · p. 2
- The AAA-based approach described in Huang et al. (2023) is considered state of the art in analytic continuation and has been cited extensively.Source: Research impact statement · p. 2
- adapol was shown to yield a more compact pole approximation than generic DLR for a fixed, given Green’s function.The passage describes generic DLR as an exponential-in-β improvement over naive uniform frequency grids.Source: Research impact statement · p. 2
AI usage disclosure
The authors used generative AI tools to assist with package development materials, then reviewed and edited the generated content.
- Generative AI assisted with code, tests, documentation, and examples, and the authors reviewed and edited its output.Source: AI usage disclosure · p. 3