  A boundary transfer matrix formulation allows to calculate the Loschmidt echo
for one-dimensional quantum systems in the thermodynamic limit. We show that
non-analyticities in the Loschmidt echo and zeros for the Loschmidt amplitude
in the complex plane (Fisher zeros) are caused by a crossing of eigenvalues in
the spectrum of the transfer matrix. Using a density-matrix renormalization
group algorithm applied to these transfer matrices we numerically investigate
the Loschmidt echo and the Fisher zeros for quantum quenches in the XXZ model
with a uniform and a staggered magnetic field. We give examples---both in the
integrable and the non-integrable case---where the Loschmidt echo does not show
non-analyticities although the quench leads across an equilibrium phase
transition, and examples where non-analyticities appear for quenches within the
same phase. For a quench to the free fermion point, we analytically show that
the Fisher zeros sensitively depend on the initial state and can lie exactly on
the real axis already for finite system size. Furthermore, we use bosonization
to analyze our numerical results for quenches within the Luttinger liquid
phase.
