Bootstrapping Calabi-Yau Quantum Mechanics

TL;DR

This paper introduces an improved bootstrap approach for quantum mechanical systems derived from Calabi-Yau geometries, enhancing numerical precision in energy eigenvalue calculations and applicable to various models.

Contribution

The authors develop an enhanced bootstrap method using multiple operators, achieving higher accuracy in quantum systems related to Calabi-Yau geometries and beyond.

Findings

Improved numerical accuracy in energy eigenvalues.

Effective application to Calabi-Yau related quantum systems.

Versatility demonstrated on non-relativistic models.

Abstract

Recently, a novel bootstrap method for numerical calculations in matrix models and quantum mechanical systems is proposed. We apply the method to certain quantum mechanical systems derived from some well-known local toric Calabi-Yau geometries, where the exact quantization conditions have been conjecturally related to topological string theory. We find that the bootstrap method provides a promising alternative for the precision numerical calculations of the energy eigenvalues. An improvement in our approach is to use a larger set of two-dimensional operators instead of one-dimensional ones. We also apply our improved bootstrap methods to some non-relativistic models in the recent literature and demonstrate better numerical accuracies.