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The Schwinger model, or 1+1 dimensional QED, offers an interesting object ofstudy, both at zero and non-zero temperature, because of its similarities toQCD. In this proceeding, we present the a full calculation of the temperaturedependent chiral condensate of this model in the continuum limit using MatrixProduct States (MPS). MPS methods, in general tensor networks, constitute avery promising technique for the non-perturbative study of Hamiltonian quantumsystems. In the last few years, they have shown their suitability as ansatzesfor ground states and low-lying excita- tions of lattice gauge theories. Weshow the feasibility of the approach also for finite temperature, both in themassless and in the massive case.

Thermal evolution of the one-flavour Schwinger model using Matrix Product States