Direct computational approach to lattice supersymmetric quantum mechanics

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.

Comments: 23 pages, 12 figures, 4 tables