Quantum quench within the gapless phase of the spin-1/2 Heisenberg XXZ spin-chain

Understand

We consider an interaction quench in the critical spin-1/2 Heisenberg XXZ chain.

• We numerically compute the time evolution of the two-point correlation functions of spin operators in the thermodynamic limit and compare the results to predictions obtained in the framework of the Luttinger liquid approximation.
• We find that the transverse correlation function $\langle S^x_jS^x_{j+\ell}\rangle$ agrees with the Luttinger model prediction to a surprising level of accuracy.
• The agreement for the longitudinal two-point function $\langle S^z_jS^z_{j+\ell}\rangle$ is found to be much poorer.