Calculation of the ground-state energy of the one-dimensional quantum ising model represented in matrix-product states

Abstract

We calculate the ground-state energy of the one-dimensional quantum Ising model in a transverse field by using the matrix-product state representation by using the imaginary time-evolving block decimation to minimize the energy. From a detailed investigation of the block energy, we find that small values of the time steps involved in the Suzuki-Trotter decompositions are crucial to reducing the truncation error. Large bond dimensions are also necessary to avoid falling into local, false ground states. In the limit of large bond dimensions and small time steps, the block energy approaches the exact value for an infinite system. For sufficiently large bond dimensions, the second derivative of the energy shows a logarithmically-diverging behavior, as theoretically predicted.