Quantum Phase Transition Critical Phenomenon And The Tensor Network Representations Research

We study the quantum phase transitions of the one dimensional quantum many-body systems by employing the infinite tensor network algorithm. Much interest have been attracted in the study of zero temperature phase transition phenomena in correlated many body system. Tensor network representation of quantum many-body wave functions provides an efficient way to classically simulate quantum many-body systems.Tensor network algorithm provide a convenient playground for investigating novel types of quantum phase transitions which can’t be investigated in the traditional framework. We provided various example of such QPTs and it is easy to construct two predetermined MPS and associated parent Hamiltonians, carry on imaginary time evolved, acquired the ground state wave function of the system. By the symmetry of model, the TN representation of quantum many-body wave functions provides a powerful means to efficiently simulate infinite-size quantum lattice systems in one or higher spatial dimensions.Two novel approaches to study QPTs have been proposed from a quantum information perspective, namely entanglement and fidelity. The approximation ground-state wave functions in the thermodynamic limit are obtained by employing the infinite tensor net-work algorithm. The bifurcation in ground-state fidelity per lattice site of spin quantum system has been studied in this thesis, from which the transition point and its critical natures are obtained exactly.The quantum models have been studied in this thesis include:one-dimensional two-spin quantum many-body system model, which Hamiltonian are we also calculate one-dimensional quantum systems von Neumann entropy, the ground-state fidelity per lattice site, scaling relation between von Neumann entropy of critical point and truncation dimensions. We also calculate the ground-state fidelity per lattice site for two-spatial dimension quantum models. We propose two concepts, spontaneous symmetry breaking and pseudo-order parameter. The computational results of the values reveal that the tensor network representation is right and viable.