Entanglement in a Dimerized Antiferromagnetic Heisenberg Chain

TL;DR

This paper investigates entanglement in a dimerized antiferromagnetic Heisenberg spin-1/2 chain, showing how the entanglement gap varies with parameters and identifying conditions for entanglement presence.

Contribution

It introduces a method to quantify entanglement via the entanglement gap and explores how it depends on the alternation parameter and temperature in the chain.

Findings

Entanglement gap increases with the alternation parameter.

Thermal energy can serve as a witness for entanglement at certain temperatures.

No inter-dimer entanglement exists if the alternation parameter is below a critical value.

Abstract

The entanglement properties in an antiferromagnetic dimerized Heisenberg spin-1/2 chain are investigated. The entanglement gap, which is the difference between the ground-state energy and the minimal energy that any separable state can attain, is calculated to detect the entanglement. It is found that the entanglement gap can be increased by varying the alternation parameter. Through thermal energy, the witness of the entanglement can determine a characteristic temperature below that an entangled state can be obtained. The entanglement detected by the energy can provide a lower bound for that determined by the concurrence. If the alternation parameter is smaller than a critical value, there is always no inter-dimer entanglement in the chain.