Ising Universality Quantum Spin Chains Based On The Finite Matrix Product State Representations

In this thesis, we have developed a scheme to efficiently compute the GE per lattice site and von Neumann Entropy for quantum many body spin systems on a periodic finite-size chain in the context of a tensor network algorithm based on the matrix product state representations. The computational cost does not depend on the chain size. A systematic test is performed for three prototypical critical quantum spin chains belonging to the same Ising universality class and one non-Ising universality class. The simulation results lend strong support to the previous claim 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. For all the models tested, the simulated g is compared to the exact g factor from conformal field theory, with the relative error less than 1.1×10^-2.