Time-dependent variational principle for quantum lattices
  We develop a new algorithm based on the time-dependent variational principle applied to matrix product states to efficiently simulate the real- and imaginary time dynamics for infinite one-dimensional quantum lattice systems. This procedure: (1) is argued to be optimal; (2) does not rely on the Trotter decomposition and thus has no Trotter error; (3) explicitly preserves all symmetries and conservation laws; and (4) has low computational complexity. The algorithm is illustrated using both imaginary time and real-time examples. 
Jutho Haegeman, J. Ignacio Cirac, Tobias J. Osborne, Iztok Pizorn,   Henri Verschelde and Frank Verstraete
cond-mat.str-el cond-mat.stat-mech quant-ph