Detailed calculation of the average work done in a ground state quench of the quantum Ising model
A detailed derivation of the exact expression for the average work done in a transverse field quench of the quantum Ising model ground state is presented. In the thermodynamic limit, it is proved that the average work done generally has inflection points at the critical field for the pre-quench quantum phase transition. The first divergent field derivative is calculated and is shown to diverge logarithmically. We also demonstrate that the average work done is equal to the product of the transverse magnetization of the pre-quench ground state and the change in the magnetic field.