PauliTrace[exp] is the head of Pauli traces. By default
the trace is not evaluated. The evaluation occurs only when the option
PauliTraceEvaluate is set to True. It is
recommended to use PauliSimplify, which will automatically
evaluate all Pauli traces in the input expression.
PauliTrace[CSI[i, j, k, l]]\text{tr}\left(\overline{\sigma }^i.\overline{\sigma }^j.\overline{\sigma }^k.\overline{\sigma }^l\right)
PauliTrace[CSI[i, j, k, l], PauliTraceEvaluate -> True]2 \left(\bar{\delta }^{il} \bar{\delta }^{jk}-\bar{\delta }^{ik} \bar{\delta }^{jl}+\bar{\delta }^{ij} \bar{\delta }^{kl}\right)
PauliTrace[CSI[i, j, k, l]]
% // PauliSimplify\text{tr}\left(\overline{\sigma }^i.\overline{\sigma }^j.\overline{\sigma }^k.\overline{\sigma }^l\right)
2 \bar{\delta }^{il} \bar{\delta }^{jk}-2 \bar{\delta }^{ik} \bar{\delta }^{jl}+2 \bar{\delta }^{ij} \bar{\delta }^{kl}