Direct computational approach to lattice supersymmetric quantum mechanics

TL;DR

This paper introduces a deterministic numerical method for calculating physical quantities in lattice supersymmetric quantum mechanics, eliminating statistical errors and achieving high precision in correlator estimates and SUSY Ward identities.

Contribution

The authors develop a transfer matrix-based numerical approach that avoids stochastic sampling, providing highly accurate results for lattice SUSY quantum mechanics.

Findings

Correlators estimated with less than 0.001% error

Effective masses match exact solutions closely

SUSY Ward identities are verified with high precision

Abstract

We propose a numerical method of estimating various physical quantities in lattice (supersymmetric) quantum mechanics. The method consists only of deterministic processes such as computing a product of transfer matrix, and has no statistical uncertainties. We use the numerical quadrature to define the transfer matrix as a finite dimensional matrix, and find that it effectively works by rescaling variable for sufficiently small lattice spacings. For a lattice supersymmetric quantum mechanics, the correlators can be estimated without statistical errors, and the effective masses coincide with the exact solution within very small errors less than 0.001%. The SUSY Ward identity is also precisely studied in compared with the Monte-Carlo method. Our method is not limited to a lattice SUSY quantum mechanics, but is also applicable to any other lattice models of quantum mechanics.