Publications | James P. F. LeBlanc

2024

Feynman diagrammatics based on discrete pole representations: A path to renormalized perturbation theories

Daria Gazizova, Lei Zhang, Emanuel Gull, and J. P. F. LeBlanc

Phys. Rev. B, Aug 2024
Symbolic determinant construction of perturbative expansions

Ibsal Assi, and J. P. F. LeBlanc

Phys. Rev. B, Mar 2024

2023

Emergent nearest-neighbor attraction in the fully renormalized interactions of the single-band repulsive Hubbard model at weak coupling

Daria Gazizova, and J. P. F. LeBlanc

Phys. Rev. B, Oct 2023

2022

Dynamic Response of an Electron Gas: Towards the Exact Exchange-Correlation Kernel

James P. F. LeBlanc, Kun Chen, Kristjan Haule, Nikolay V. Prokof’ev, and Igor S. Tupitsyn

Phys. Rev. Lett., Dec 2022

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Precise calculations of dynamics in the homogeneous electron gas (jellium model) are of fundamental importance for design and characterization of new materials. We introduce a diagrammatic Monte Carlo technique based on algorithmic Matsubara integration that allows us to compute frequency and momentum resolved finite temperature response directly in the real frequency domain using a series of connected Feynman diagrams. The data for charge response at moderate electron density are used to extract the frequency dependence of the exchange-correlation kernel at finite momenta and temperature. These results are as important for development of the time-dependent density functional theory for materials dynamics as ground state energies are for the density functional theory.
@article{PhysRevLett.129.246401, title = {Dynamic Response of an Electron Gas: Towards the Exact Exchange-Correlation Kernel}, author = {LeBlanc, James P. F. and Chen, Kun and Haule, Kristjan and Prokof'ev, Nikolay V. and Tupitsyn, Igor S.}, journal = {Phys. Rev. Lett.}, volume = {129}, issue = {24}, pages = {246401}, numpages = {5}, year = {2022}, month = dec, publisher = {American Physical Society}, doi = {10.1103/PhysRevLett.129.246401}, url = {https://link.aps.org/doi/10.1103/PhysRevLett.129.246401}, dimensions = {true}, }
LIBAMI: Implementation of algorithmic Matsubara integration

Hossam Elazab, B.D.E. McNiven, and J.P.F. LeBlanc

Computer Physics Communications, Dec 2022

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We present libami, a lightweight implementation of algorithmic Matsubara integration (AMI) written in C++. AMI is a tool for analytically resolving the sequence of nested Matsubara integrals that arise in virtually all Feynman perturbative expansions. Program summary Program Title: libami CPC Library link to program files: https://doi.org/10.17632/zkwwmbnm6m.1 Developer’s repository link: https://github.com/jpfleblanc/libami Licensing provisions: GPLv3 Programming language: C++ Nature of problem: Perturbative expansions in condensed matter systems are formulated on the imaginary frequency/time axis and are often represented as a series of Feynman diagrams, which involve a sequence of nested integrals/summations over internal Matsubara indices as well as other internal variables. Solution method: libami provides a minimal framework to symbolically generate and store the analytic solution to the temporal Matsubara sums through repeated application of multipole residue theorems. The solution can be applied to any frequency-independent interaction expansion. Once generated, the analytic solution is valid in any dimensionality with any dispersion at arbitrary temperature. Additional comments including restrictions and unusual features: Requires C++11 standard. Optional compilation with boost-multiprecision library. References [1]Amir Taheridehkordi, S.H. Curnoe, J.P.F. LeBlanc, Algorithmic Matsubara integration for Hubbard-like models, Phys. Rev. B 99 (2019) 035120.

2021

Tracking the Footprints of Spin Fluctuations: A MultiMethod, MultiMessenger Study of the Two-Dimensional Hubbard Model

Thomas Schäfer, Nils Wentzell, Fedor Š\fiimkovic, Yuan-Yao He, Cornelia Hille, and 21 more authors

Phys. Rev. X, Mar 2021

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The Hubbard model represents the fundamental model for interacting quantum systems and electronic correlations. Using the two-dimensional half-filled Hubbard model at weak coupling as a testing ground, we perform a comparative study of a comprehensive set of state-of-the-art quantum many-body methods. Upon cooling into its insulating antiferromagnetic ground state, the model hosts a rich sequence of distinct physical regimes with crossovers between a high-temperature incoherent regime, an intermediate-temperature metallic regime, and a low-temperature insulating regime with a pseudogap created by antiferromagnetic fluctuations. We assess the ability of each method to properly address these physical regimes and crossovers through the computation of several observables probing both quasiparticle properties and magnetic correlations, with two numerically exact methods (diagrammatic and determinantal quantum Monte Carlo methods) serving as a benchmark. By combining computational results and analytical insights, we elucidate the nature and role of spin fluctuations in each of these regimes. Based on this analysis, we explain how quasiparticles can coexist with increasingly long-range antiferromagnetic correlations and why dynamical mean-field theory is found to provide a remarkably accurate approximation of local quantities in the metallic regime. We also critically discuss whether imaginary-time methods are able to capture the non-Fermi-liquid singularities of this fully nested system.
@article{PhysRevX.11.011058, title = {Tracking the Footprints of Spin Fluctuations: A MultiMethod, MultiMessenger Study of the Two-Dimensional Hubbard Model}, author = {Sch\"afer, Thomas and Wentzell, Nils and \ifmmode \check{S}\else \v{S}\fi{}imkovic, Fedor and He, Yuan-Yao and Hille, Cornelia and Klett, Marcel and Eckhardt, Christian J. and Arzhang, Behnam and Harkov, Viktor and Le R\'egent, Fran\ifmmode \mbox{\c{c}}\else \c{c}\fi{}ois-Marie and Kirsch, Alfred and Wang, Yan and Kim, Aaram J. and Kozik, Evgeny and Stepanov, Evgeny A. and Kauch, Anna and Andergassen, Sabine and Hansmann, Philipp and Rohe, Daniel and Vilk, Yuri M. and LeBlanc, James P. F. and Zhang, Shiwei and Tremblay, A.-M. S. and Ferrero, Michel and Parcollet, Olivier and Georges, Antoine}, journal = {Phys. Rev. X}, volume = {11}, issue = {1}, pages = {011058}, numpages = {53}, year = {2021}, month = mar, publisher = {American Physical Society}, doi = {10.1103/PhysRevX.11.011058}, url = {https://link.aps.org/doi/10.1103/PhysRevX.11.011058}, dimensions = {true}, }

2019

Algorithmic Matsubara integration for Hubbard-like models

Amir Taheridehkordi, S. H. Curnoe, and J. P. F. LeBlanc

Phys. Rev. B, Jan 2019

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We present an algorithm to evaluate Matsubara sums for Feynman diagrams composed of bare Green’s functions with single-band dispersions and local 𝑈 Hubbard interaction vertices. The algorithm provides an exact construction of the analytic result for the frequency integrals of a diagram that can then be evaluated for all parameters 𝑈, temperature 𝑇, chemical potential 𝜇, external frequencies, and internal/external momenta. This method allows for symbolic analytic continuation of results to the real frequency axis, avoiding any ill-posed numerical procedure. This method can also be used to simultaneously evaluate diagrams throughout the entire 𝑇−𝑈−𝜇 phase space of Hubbard-like models even in the 𝑇=0 limit at minimal computational expense.
@article{PhysRevB.99.035120, title = {Algorithmic Matsubara integration for Hubbard-like models}, author = {Taheridehkordi, Amir and Curnoe, S. H. and LeBlanc, J. P. F.}, journal = {Phys. Rev. B}, volume = {99}, issue = {3}, pages = {035120}, numpages = {5}, year = {2019}, month = jan, publisher = {American Physical Society}, doi = {10.1103/PhysRevB.99.035120}, url = {https://link.aps.org/doi/10.1103/PhysRevB.99.035120}, dimensions = {true}, }

2015

Fluctuation Diagnostics of the Electron Self-Energy: Origin of the Pseudogap Physics

O. Gunnarsson, T. Schäfer, J. P. F. LeBlanc, E. Gull, J. Merino, and 3 more authors

Phys. Rev. Lett., Jun 2015

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We demonstrate how to identify which physical processes dominate the low-energy spectral functions of correlated electron systems. We obtain an unambiguous classification through an analysis of the equation of motion for the electron self-energy in its charge, spin, and particle-particle representations. Our procedure is then employed to clarify the controversial physics responsible for the appearance of the pseudogap in correlated systems. We illustrate our method by examining the attractive and repulsive Hubbard model in two dimensions. In the latter, spin fluctuations are identified as the origin of the pseudogap, and we also explain why 𝑑-wave pairing fluctuations play a marginal role in suppressing the low-energy spectral weight, independent of their actual strength.
@article{PhysRevLett.114.236402, title = {Fluctuation Diagnostics of the Electron Self-Energy: Origin of the Pseudogap Physics}, author = {Gunnarsson, O. and Sch\"afer, T. and LeBlanc, J. P. F. and Gull, E. and Merino, J. and Sangiovanni, G. and Rohringer, G. and Toschi, A.}, journal = {Phys. Rev. Lett.}, volume = {114}, issue = {23}, pages = {236402}, numpages = {6}, year = {2015}, month = jun, publisher = {American Physical Society}, doi = {10.1103/PhysRevLett.114.236402}, url = {https://link.aps.org/doi/10.1103/PhysRevLett.114.236402}, dimensions = {true}, }
Solutions of the Two-Dimensional Hubbard Model: Benchmarks and Results from a Wide Range of Numerical Algorithms

J. P. F. LeBlanc, Andrey E. Antipov, Federico Becca, Ireneusz W. Bulik, Garnet Kin-Lic Chan, and 20 more authors

Phys. Rev. X, Dec 2015

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Numerical results for ground-state and excited-state properties (energies, double occupancies, and Matsubara-axis self-energies) of the single-orbital Hubbard model on a two-dimensional square lattice are presented, in order to provide an assessment of our ability to compute accurate results in the thermodynamic limit. Many methods are employed, including auxiliary-field quantum Monte Carlo, bare and bold-line diagrammatic Monte Carlo, method of dual fermions, density matrix embedding theory, density matrix renormalization group, dynamical cluster approximation, diffusion Monte Carlo within a fixed-node approximation, unrestricted coupled cluster theory, and multireference projected Hartree-Fock methods. Comparison of results obtained by different methods allows for the identification of uncertainties and systematic errors. The importance of extrapolation to converged thermodynamic-limit values is emphasized. Cases where agreement between different methods is obtained establish benchmark results that may be useful in the validation of new approaches and the improvement of existing methods.
@article{PhysRevX.5.041041, title = {Solutions of the Two-Dimensional Hubbard Model: Benchmarks and Results from a Wide Range of Numerical Algorithms}, author = {LeBlanc, J. P. F. and Antipov, Andrey E. and Becca, Federico and Bulik, Ireneusz W. and Chan, Garnet Kin-Lic and Chung, Chia-Min and Deng, Youjin and Ferrero, Michel and Henderson, Thomas M. and Jim\'enez-Hoyos, Carlos A. and Kozik, E. and Liu, Xuan-Wen and Millis, Andrew J. and Prokof'ev, N. V. and Qin, Mingpu and Scuseria, Gustavo E. and Shi, Hao and Svistunov, B. V. and Tocchio, Luca F. and Tupitsyn, I. S. and White, Steven R. and Zhang, Shiwei and Zheng, Bo-Xiao and Zhu, Zhenyue and Gull, Emanuel}, collaboration = {Simons Collaboration on the Many-Electron Problem}, journal = {Phys. Rev. X}, volume = {5}, issue = {4}, pages = {041041}, numpages = {28}, year = {2015}, month = dec, publisher = {American Physical Society}, doi = {10.1103/PhysRevX.5.041041}, url = {https://link.aps.org/doi/10.1103/PhysRevX.5.041041}, dimensions = {true}, }