  We introduce a numerical approach to calculate the statistics of work done on
1D quantum lattice systems initially prepared in thermal equilibrium states.
This approach is based on two tensor-network techniques: Time Evolving Block
Decimation (TEBD) and Minimally Entangled Typical Thermal States (METTS). The
former is an efficient algorithm used to simulate the dynamics of 1D quantum
lattice systems, while the latter a finite-temperature algorithm for generating
a set of typical states representing the Gibbs canonical ensemble. As an
illustrative example, we apply this approach to the Ising chain in mixed
transverse and longitudinal fields. Under an arbitrary protocol, the moment
generating function of the work can be obtained, from which the work moments
are numerically calculated and the quantum Jarzynski equality can be tested.
Moreover, the numerical approach is also adapted to test the universal quantum
work relation involving a functional of an arbitrary observable.
