Partitioning technique for a discrete quantum system

TL;DR

This paper introduces a partitioning technique for quantum discrete systems, allowing the effective Hamiltonian of a complex graph to be constructed from simpler subgraphs with added potentials, simplifying analysis.

Contribution

The paper presents a novel partitioning method for quantum graphs, enabling easier computation of the effective Hamiltonian by reducing the system to a central graph with modified potentials.

Findings

Effective Hamiltonian can be constructed by adding potentials on branch-root nodes.

The method simplifies analysis of complex quantum graphs.

Exactly solvable models demonstrate the technique's validity.

Abstract

We develop the partitioning technique for quantum discrete systems. The graph consists of several subgraphs: a central graph and several branch graphs, with each branch graph being rooted by an individual node on the central one. We show that the effective Hamiltonian on the central graph can be constructed by adding additional potentials on the branch-root nodes, which generates the same result as does the the original Hamiltonian on the entire graph. Exactly solvable models are presented to demonstrate the main points of this paper.