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arXiv · 0911.5145

Properties of Quantum Systems via Diagonalization of Transition Amplitudes I: Discretization Effects

Ivana Vidanovic·Aleksandar Bogojevic·Aleksandar Belic
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Abstract

We analyze the method for calculation of properties of non-relativistic quantum systems based on exact diagonalization of space-discretized short-time evolution operators. In this paper we present a detailed analysis of the errors associated with space discretization. Approaches using direct diagonalization of real-space discretized Hamiltonians lead to polynomial errors in discretization spacing $\Delta$. Here we show that the method based on the diagonalization of the short-time evolution operators leads to substantially smaller discretization errors, vanishing exponentially with $1/\Delta^2$. As a result, the presented calculation scheme is particularly well suited for numerical studies of few-body quantum systems. The analytically derived discretization errors estimates are numerically shown to hold for several models. In the followup paper [1] we present and analyze substantial improvements that result from the merger of this approach with the recently introduced effective-action scheme for high-precision calculation of short-time propagation.

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Ivana Vidanovic, Aleksandar Bogojevic, Aleksandar Belic. 2009-11-26. Properties of Quantum Systems via Diagonalization of Transition Amplitudes I: Discretization Effects. https://doi.org/10.1103/physreve.80.066705

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