Simulation of time evolution in an integrable system, XXZ model: energy eigenvalues.
In this article, we will calculate the energy eigenvalues, which we did not do in the previous article. the XXZ system is well known as an integrable system. In the previous article, it was shown that the probability of the existence of a spin-relaxed state increases when the value of delta is set to 1, while it does not occur when the value of delta is set to 2. Figures 1 and 2 show the time evolution of the energy at delta = 1 and 2, respectively. The results show that the energy periodically changes around -5 for Δ=1 and around -6 for Δ=2 while oscillating. However, for Δ=1, it is assumed to go directly to the eigenvalue of the state where all spins are downward.
Figure 1: Time evolution of the energy at Δ=1. The lines represent the data averaged over the previous and next values.
Figure 2: Time evolution of energy at Δ=2. The line shows the data averaged over the previous and next values.
The XXZ system is the simplest integrable system. For other systems that can be represented as spin systems, simulators such as blueqat can easily simulate the contents of the paper. Therefore, I am planning to do some more simulations in addition to this one.