The Discrete Bootstrap for Quantum Thermodynamics

Abstract

A novel bootstrap method is exemplified by lattice theories and quantum mechanics. Positivity of expectation values combined with sets of non-trivial constraint equations and semidefinite optimization rigorously and precisely bound correlation functions. Starting with the example of a one-dimensional integral, the technique is built upon to extract limit cycles in a two-dimensional classical dynamical system and spin correlation functions in the Statistical Ising Model. Further positivity constraints and simplifications arising in a large rank limit are implemented to bound the energy expectation value as a function of temperature in Matrix Quantum Mechanics. Along the way, the S-matrix of Chern-Simons-matter theory is computed as an example of computational simplification at large gauge group rank.