Engineering topics
Krieg, Stefan
Publications and source records attributed to Krieg, Stefan.
Transverse momentum-dependent parton distributions for longitudinally polarized nucleons from domain wall fermion calculations at the physical pion mass
Previous Lattice QCD calculations of nucleon transverse momentum-dependent parton distribu?tions (TMDs) focused on the case of transversely polarized nucleons, and thus did not encompass two leading-twist TMDs associated with longitudinal polarization, namely, the helicity TMD and the worm-gear TMD corresponding to transversely polarized quarks in a longitudinally polarized nucleon. Based on a definition of TMDs via hadronic matrix elements of quark bilocal operators containing staple-shaped gauge connections, TMD observables characterizing the aforementioned two TMDs are evaluated, utilizing an RBC/UKQCD domain wall fermion ensemble at the physical pion mass.
Antiferromagnetic character of the quantum phase transition in the Hubbard model on the honeycomb lattice
In this work we provide a unified, comprehensive treatment of all operators that contribute to the antiferromagnetic, ferromagnetic, and charge-density-wave structure factors and order parameters of the hexagonal Hubbard Model. We use the Hybrid Monte Carlo algorithm to perform a systematic, carefully controlled analysis in the temporal Trotter error and of the thermodynamic limit. We expect our findings to improve the consistency of Monte Carlo determinations of critical exponents. We perform a data collapse analysis and determine the critical exponent β = 0.898 (37) for the semimetal-Mott insulator transition in the hexagonal Hubbard Model. Our methods are applicable to a wide range of lattice theories of strongly correlated electrons.
Machine learning to alleviate Hubbard-model sign problems
Lattice Monte Carlo calculations of interacting systems on nonbipartite lattices exhibit an oscillatory imaginary phase known as the phase or sign problem, even at zero chemical potential. One method to alleviate the sign problem is to analytically continue the integration region of the state variables into the complex plane via holomorphic flow equations. For asymptotically large flow times, the state variables approach manifolds of constant imaginary phase known as Lefschetz thimbles. Furthermore, flowing such variables and calculating the ensuing Jacobian is a computationally demanding procedure. In this paper, we demonstrate that neural networks can be trained to parametrize suitable manifolds for this class of sign problem and drastically reduce the computational cost for different severely afflicted small volume systems. In particular, we apply our method to the Hubbard model on the triangle and tetrahedron, both of which are nonbipartite. At strong interaction strengths and modest temperatures, the tetrahedron suffers from a severe sign problem that cannot be overcome with standard reweighting techniques, while it quickly yields to our method. We benchmark our results with exact calculations and comment on future directions of this work.
Semimetal–Mott insulator quantum phase transition of the Hubbard model on the honeycomb lattice
We take advantage of recent improvements in the grand canonical hybrid Monte Carlo algorithm, to perform a precision study of the single-particle gap in the hexagonal Hubbard model, with on-site electron-electron interactions. After carefully controlled analyses of the Trotter error, the thermodynamic limit, and finite-size scaling with inverse temperature, we find a critical coupling of U c /κ = 3.834(14) and the critical exponent zν = 1.185(43). Under the assumption that this corresponds to the expected antiferromagnetic Mott transition, we are also able to provide a preliminary estimate β = 1.095(37) for the critical exponent of the order parameter. We consider our findings in view of the SU(2) Gross-Neveu, or chiral Heisenberg, universality class. Here, we also discuss the computational scaling of the hybrid Monte Carlo algorithm, and possible extensions of our work to carbon nanotubes, fullerenes, and topological insulators.
Low-energy pion-nucleon scattering and the Δ resonance in lattice QCD
We report on our investigation of low-energy pion-nucleon scattering from lattice QCD with Wilson type fermions. Our focus is on the isospin I = 3/2 channel, which couples to the Delta resonance. We discuss our calculations aiming at the extraction of the Delta resonance mass, width and effective coupling at pion mass 250 MeV, using the Lüscher finite-volume method to extract the phase shift δ J=3/2,l=1 .