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We present an algorithm to study mixed-state dynamics in one-dimensionalquantum lattice systems. The algorithm can be used, e.g., to construct thermalstates or to simulate real time evolutions given by a generic master equation.Its two main ingredients are (i) a superoperator renormalization scheme toefficiently describe the state of the system and (ii) the time evolving blockdecimation (TEBD) technique to efficiently update the state during a timeevolution. The computational cost of a simulation increases significantly withthe amount of correlations between subsystems but it otherwise depends onlylinearly in the system size. We present simulations involving quantum spins andfermions in one spatial dimension.Comment: See also F. Verstraete et al. cond-mat/040642

Mixed-State Dynamics in One-Dimensional Quantum Lattice Systems: A Time-Dependent Superoperator Renormalization Algorithm