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.

23 pages, 12 figures, 4 tables

References in corpus (17)

• Tensor renormalization group approach to 2D classical lattice models
• Grassmann Tensor Renormalization Group Approach to One-Flavor Lattice Schwinger Model
• Critical behavior of lattice Schwinger model with topological term at $\theta =\pi$ using Grassmann tensor renormalization group
• Grassmann tensor renormalization group for one-flavor lattice Gross-Neveu model with finite chemical potential
• Low-dimensional Supersymmetric Lattice Models
• Berezinskii-Kosterlitz-Thouless transition in lattice Schwinger model with one flavor of Wilson fermion
• Observing dynamical supersymmetry breaking with euclidean lattice simulations
• Higher order tensor renormalization group for relativistic fermion systems
• Calculation of fermionic Green functions with Grassmann higher-order tensor renormalization group
• Two-Dimensional Wess-Zumino Models at Intermediate Couplings
• Dual representation of lattice QCD with worldlines and worldsheets of abelian color fluxes
• A lattice study of N=2 Landau-Ginzburg model using a Nicolai map
• Spontaneous supersymmetry breaking in the two-dimensional N=1 Wess-Zumino model
• Kramers-Wannier duality and worldline representation for the SU(2) principal chiral model
• Exact Lattice Supersymmetry at the Quantum Level for $N=2$ Wess-Zumino Models in 1- and 2-Dimensions
• Supersymmetry restoration in lattice formulations of 2D $\mathcal{N}=(2,2)$ WZ model based on the Nicolai map
• An Alternative Lattice Field Theory Formulation Inspired by Lattice Supersymmetry

Cited by in corpus (8)

• Tensor network analysis of critical coupling in two dimensional ${\varphi }^4$ theory
• Progress and prospects of lattice supersymmetry
• Lattice studies of supersymmetric gauge theories
• Tensor network approach to 2d Lorentzian quantum Regge calculus
• Lattice study of supersymmetry breaking in N=2 supersymmetric quantum mechanics
• Complex Langevin Dynamics and Supersymmetric Quantum Mechanics
• Numerical analyses of N=2 supersymmetric quantum mechanics with cyclic Leibniz rule on lattice
• Probing Non-perturbative Supersymmetry Breaking through Lattice Path Integrals