  We present our recent results for the tensor network (TN) approach to lattice
gauge theories. TN methods provide an efficient approximation for quantum
many-body states. We employ TN for one dimensional systems, Matrix Product
States, to investigate the 1-flavour Schwinger model. In this study, we compute
the chiral condensate at finite temperature. From the continuum extrapolation,
we obtain the chiral condensate in the high temperature region consistent with
the analytical calculation by Sachs and Wipf.
