Tags: Numerics

Check out this plot:

Plot

Q: What is wrong?

A: The value of the graph should start as 1 (not 0.8) at time equal 0 for the positions where the up-signs are located.

Why?

My best guess is that the Bethe Equations (BE) were not solved to good enough precision, i.e. the solutions we’re not calibrated well enough. Recall that the BE are only solved numerically as the limit point of a sequence that converges to a solution due to the Fixed Point Theorem (FPT).

In the code, we only approximate the limit points by computing a term in the sequence with a large enough index. Thus, the values from the code are only approximations to the exact solutions.

Remark

The plots with \(\Delta=0\) don’t suffer from this error since the sequence in that case is constant, i.e. the sequence converges by the first term.

Next steps

  • In the code, we have a parameter that determines the index of the sequence. We need to make that higher.