Quantum quench within the gapless phase of the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mtext>spin</mml:mtext><mml:mo>−</mml:mo><mml:mfrac><mml:mn>1</mml:mn><mml:mn>2</mml:mn></mml:mfrac></mml:math>Heisenberg XXZ spin chain

We consider an interaction quench in the critical $\text{spin}\ensuremath{-}\frac{1}{2}$ 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 $\ensuremath{\langle}{S}_{j}^{x}{S}_{j+\ensuremath{\ell}}^{x}\ensuremath{\rangle}$ agrees with the Luttinger model prediction to a surprising level of accuracy. The agreement for the longitudinal two-point function $\ensuremath{\langle}{S}_{j}^{z}{S}_{j+\ensuremath{\ell}}^{z}\ensuremath{\rangle}$ is found to be much poorer. We speculate that this difference between transverse and longitudinal correlations has its origin in the locality properties of the respective spin operator with respect to the underlying fermionic modes.

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