A one dimensional model showing a quantum phase transition based on a singular potential

TL;DR

This paper investigates a one-dimensional quantum system with a singular potential and various regular interactions, revealing a novel quantum phase transition influenced by quantum non-locality.

Contribution

It introduces a new type of quantum phase transition in a one-dimensional model with singular potential, highlighting the role of quantum non-locality.

Findings

Existence of a unique bound state in electric field case

Shift of ground state and appearance of quasibound states with electric field

Discovery of a novel quantum phase transition in harmonic oscillator case

Abstract

We study a one-dimensional singular potential plus three types of regular interactions: constant electric field, harmonic oscillator and infinite square well. We use the Lippman-Schwinger Green function technique in order to search for the bound state energies. In the electric field case the unique bound state coincides with that found in an earlier study as the field is switched off. For non-zero field the ground state is shifted and positive energy "quasibound states" appear. For the harmonic oscillator we find a quantum phase transition of a novel type. This behavior does not occur in the corresponding case of an infinite square well and demonstrates the influence of quantum non-locality.