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In this paper, we describe a refined matrix product representation for many-body states that are invariant under SU(2) transformations and use it to extend the time-evolving block decimation (TEBD) algorithm to the simulation of time evolution in the presence of an SU(2) symmetry. The resulting algorithm, when tested in a critical quantum spin chain, proved to be more efficient than the standard TEBD. [ABSTRACT FROM AUTHOR]

An efficient scheme for computing the geometric entanglement (GE) per lattice site for quantum many-body systems on a periodic finite-size chain is proposed in the context of a tensor network algorithm based on matrix product state representations. It has been systematically tested for three prototypical critical quantum spin chains, which belong to the same Ising universality class. The simulation results lend strong support to the previous claim (Shi et al 2010 New J. Phys. 12 025008; Stéphan et al 2010 Phys. Rev. B 82 180406R) that the leading finite-size correction to the GE per lattice site is universal, with its remarkable connection to the celebrated Affleck-Ludwig boundary entropy corresponding to a conformally invariant boundary condition. [ABSTRACT FROM AUTHOR]

The global geometric entanglement (GE) is studied in the context of newly developed tensor network algorithms for finite systems. For onedimensional quantum spin systems it is found that, at criticality, the leading finite-size correction to the global GE per site behaves as b/n, where n is the size of the system and b a given coefficient. Our conclusion is based on the computation of the GE per spin for the quantum Ising model in a transverse magnetic field and for the spin-1/2 XXZ model. We also discuss the possibility of coefficient b being universal. [ABSTRACT FROM AUTHOR]