Strongly interacting few-body systems from lattice stochastic methods

Abstract

Lattice Monte Carlo plays an important role for non-perturbative descriptions of strong interactions. Despite its success in recent years, some fundamental challenges remain. Two of them are investigated in this work, namely simulating few-baryon systems from first principles and the phase problem that plagues Monte Carlo in many cases. <br /> Three nucleon forces are a major source of uncertainty in the equation of state of neutron stars and the determination of the location of the neutron dripline, for example However, lattice Quantum Chromodynamics calculations are restricted to relatively small systems by a factorial increase of Wick contractions between quarks and notoriously poor signal-to-noise ratios. Multi nucleon s-wave systems have been calculated from Lattice Quantum Chromodynamics in the past. The three-neutron system was not included in those studies, however. This thesis describes an approach for the measurement of p-wave three-neutron correlation functions. Baryon blocks are used as a means for a systematic momentum projection onto p-waves. The measurement program is computer generated in order to handle the large number of Wick contractions and optimizes the usage of baryon blocks. Correlators of two nucleons and three neutrons are measured and their energy shifts with respect to single neutrons are calculated. Unsurprisingly, statistical noise dominates the novel three-neutron correlators. <br /> A different application of lattice Monte Carlo is the simulation of the Hubbard model of low dimensional lattices. Lattice Monte Carlo, and in particular Hybrid Monte Carlo, simulations of the Hubbard model are not always ergodic. Some lattice formulations of the model suffer from severe ergodicity problems and should thus be avoided. Others are formally not ergodic because of potential barriers in phase space. This does not pose a problem in practice, however, as those barriers can be crossed by a properly tuned Hybrid Monte Carlo. A new Monte Carlo updating scheme is presented which allows jumping across these barriers, thus further enhancing phase space coverage. Numerical tests are performed on small, representative lattices, showing definitive improvement over non-ergodic simulations. <br /> Finally, the complex phase problem prevents the application of Monte Carlo to doped materials as these systems exhibit a non-zero chemical potential. A similar phase problem occurs with non-bipartite lattices like fullerenes. An algorithm for alleviating this phase problem is presented and implemented. Neural networks are trained on field configurations generated via holomorphic flow. Path integrals on the manifold defined through these networks have a reduced phase problem. Compared to previous applications of this method, the training procedure is simplified to decrease the required computer resources. Hybrid Monte Carlo is augmented with these networks and used to generate ensembles of field configurations on the non-bipartite triangle and tetrahedron lattices; the latter exhibits a phase problem so severe that reliable results cannot be obtained with standard Monte Carlo simulations but are readily obtainable when neural networks are included. Various correlation functions are measured on these ensembles and are found to agree with results from exact diagonalization of the Hamiltonian, providing evidence for the correctness of the new algorithm.