High-precision bootstrap of multi-matrix quantum mechanics

TL;DR

This paper develops a high-precision bootstrap method for multi-matrix quantum mechanics, achieving extremely accurate results for simple observables in the confining phase, surpassing previous lattice Monte Carlo simulations.

Contribution

It introduces a matrix bootstrap approach with non-linear relaxation for multi-matrix models, providing unprecedented precision in calculating observables.

Findings

Achieved up to 8 significant digits in observable estimates.

Extended constraints up to level 14, improving accuracy.

Surpassed lattice Monte Carlo results in precision.

Abstract

We consider matrix quantum mechanics with multiple bosonic matrices, including those obtained from dimensional reduction of Yang-Mills theories. Using the matrix bootstrap, we study simple observables like $\langle \mathop{tr} X^2 \rangle$ in the confining phase of the theory in the infinite $N$ limit. By leveraging the symmetries of these models and using non-linear relaxation, we consider constraints up to level 14, e.g., constraints from traces of words of length $\le 14$. Our results are more precise than large $N$, continuum extrapolations of lattice Monte Carlo simulations, including an estimate of certain simple observables up to 8 significant digits.