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Abstract:
In this work, we investigate quenches in a free-fermion chain with long-range hopping, which decay with the distance with an exponent nu and has range D. By exploring the exact solution of the model, we found that the dynamic free energy is nonanalytical in the thermodynamic limit, whenever the sudden quench crosses the equilibrium quantum critical point. We were able to determine the nonanalyticities of dynamic free energy f (t) at some critical times t(c) by solving nonlinear equations. We also show that the Yang-Lee-Fisher (YLF) zeros cross the real-time axis at those critical times. We found that the number of nontrivial critical times, N-s, depends on nu and D. In particular, we show that for small nu and large D the dynamic free energy presents nonanalyticities in any time interval Delta t similar to 1/D << 1, i.e., there are nonanalyticities at almost all times. For the spacial case nu = 0, we obtain the critical times in terms of a simple expression of the model parameters and also show that f (t) is nonanalytical even for finite system under antiperiodic boundary condition, when we consider some special values of quench parameters. We also show that, generically, the first derivative of the dynamic free energy is discontinuous at the critical time instant when the YLF zeros are nondegenerate. On the other hand, when they become degenerate, all derivatives of f (t) exist at the associated critical instant.
