Anomalous behavior of magnetic susceptibility obtained by quench experiments in isolated quantum systems

We examine how the magnetic susceptibility obtained by the quench experiment on isolated quantum systems is related to the isothermal and adiabatic susceptibilities defined in thermodynamics. Under the conditions that the modified forms of eigenstate thermalization hypothesis (ETH) are satisfied, together with some additional natural conditions, we prove that for translationally invariant systems the quench susceptibility as a function of the wavevector k is discontinuous at k=0. Moreover, its values at k=0 and the k to 0 limit coincide with the adiabatic and the isothermal susceptibilities, respectively. We give numerical predictions on how these particular behaviors can be observed in experiments on the XYZ spin chain with tunable parameters, and how they deviate when the conditions are not fully satisfied.