Scaling the semidefinite program solver SDPB

Abstract

We present enhancements to SDPB, an open source, parallelized, arbitrary precision semidefinite program solver designed for the conformal bootstrap. The main enhancement is significantly improved performance and scalability using the Elemental library and MPI. The result is a new version of SDPB that runs on multiple nodes with hundreds of cores with excellent scaling, making it practical to solve larger problems. We demonstrate performance on a moderate-size problem in the 3d Ising CFT and a much larger problem in the O(2) Model.

Rigorous bounds on irrelevant operators in the 3d Ising model CFT

“…The polynomial matrix problem is in turn written as a Semi-Definite Program in the standard manner and solved using SDPB[10,39]. See Appendix B for the choice of numerical parameters we used.…”

Bootstrapping (D, D) Conformal Matter

“…The bounds are then obtained from the semi-definite program in equation ( 27) using the solver sdpb [68,69] (version 2.3.1) with parameters:…”

“…There are nowadays standard tools to solve semidefinite programs, in particular a numerical solver, SDPB, was specifically created for applications to the numerical bootstrap [68,69]. In Appendix A, we explain how we implemented and solved the semi-definite program numerically, leading to the results found in the next sections.…”

Precision Bootstrap for the $\mathcal{N}=1$ Super-Ising Model

“…Our setup for the conformal bootstrap builds on the previous works [31,2,3] and is identical to the one described in [2], which is an application of the "long multiplet bootstrap" idea initiated in [32]. In particular, we use the 4 crossing relations arising from the correlators σσσσ and σσ , where σ and are the parity-odd and parity-even scalars contained in the leading B Under these assumptions we have used a Delaunay triangulation search [33] and the convex optimization solver sdpb [34,35] to compute islands in the {∆ σ , ∆ σ } plane at derivative orders Λ = 35,43,51,59, improving on the Λ = 27 computation performed in [2]. The parameters used for these computations are described in Appendix A.…”