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In this thesis, we introduce new tools for the conformal bootstrap, autobootand qboot. Each tool solves a different step in the whole computational stack,and combined with an existing efficient tool SDPB which solves semidefiniteprogramming (SDP), our tools make it easier to study conformal field theorieswith more complicated global symmetries and with more general spectra. In theintroduction, we review how the conformal bootstrap method gives richinformation about the theory at the fixed point of renormalization group, or inother words, the critical phenomena such as the Ising model at criticality. Thefollowing three sections focus on the theories behind the implementation ofautoboot and qboot, and the explicit implementation, freely available athttps://github.com/selpoG/autoboot/ and https://github.com/selpoG/qboot/, isdiscussed in section 5. We also have two applications in the last section, theIsing model and the O(2) vector model in three dimensions, each of them hasclose relationship with a physical system in the real world.

An Automated Generation of Bootstrap Equations for Numerical Study of Critical Phenomena