Bulletin of the American Physical Society
APS March Meeting 2018
Monday–Friday, March 5–9, 2018; Los Angeles, California
Session H34: Precision Many Body Physics I
2:30 PM–5:30 PM,
Tuesday, March 6, 2018
LACC Room: 409A
Sponsoring Units: DCOMP DAMOP DCMP
Chair: Lubos Mitas, North Carolina State Univ
Abstract: H34.00009 : Unbiased Many-Body calculations with Dyson-Schwinger equations: A novel approach to functional integro-differential equations.
4:30 PM–4:42 PM
We show how to derive a suitable closed set of functional integro-differential equations based on Dyson-Schwinger equations and introduce the necessary tools to find an unbiased numerical solution. The key concepts are the Homotopy Analysis Method and the adaptation of this semi-analytic method from differential equations to the diagrammatic language of field theory. The resulting diagrams can be summed up by a stochastic sampling procedure. Taking all these techniques into account provides a novel approach to solve the infinite hierarchy of Dyson-Schwinger equations without any truncation.
We illustrate these ideas for the Z2 symmetric Φ4 model in 0 space-time dimensions and show results for the 2-dimensional case which undergoes a second order phase transition belonging to the Ising universality class.
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