Real-time dynamics at finite temperature by DMRG: A path-integral approach

We propose a path-integral variant of the DMRG method to calculate real-time correlation functions at arbitrary finite temperatures. To illustrate the method we study the longitudinal autocorrelation function of the $XXZ$-chain. By comparison with exact results at the free fermion point we show that our method yields accurate results up to a limiting time which is determined by the spectrum of the reduced density matrix.