# Ground state entanglement entropy for discrete-time two coupled harmonic oscillators

## TL;DR

This paper investigates how ground state entanglement entropy varies in a system of two coupled harmonic oscillators across discrete and continuous time, revealing effects of interaction strength, potential, and a cut-off in discrete-time entanglement.

## Contribution

It provides a comparative analysis of entanglement in discrete and continuous-time systems, highlighting a cut-off condition unique to discrete-time dynamics.

## Key findings

- Entanglement increases with interaction strength in both time scales.
- Harmonic potential influences the entanglement formation rate.
- Discrete-time entanglement has a cut-off, preventing maximal entanglement.

## Abstract

The ground state entanglement of the system, both in discrete-time and continuous-time cases, is quantified through the linear entropy. The result shows that the entanglement increases as the interaction between the particles increases in both time scales. It is also found that the strength of the harmonic potential affects the formation rate of the entanglement of the system. The different feature of the entanglement between continuous-time and discrete-time scales is that, for discrete-time entanglement, there is a cut-off condition. This condition implies that the system can never be in a maximally entangled state.