Degenerate Groundstates And Spontaneous Symmetry Breakings In Quantum Phase Transitions: Spin-1/2 Plaquette Chain Systems

Recently, emergent symmetry is one of fast-growing intriguing issues in many-body systems. Its roles and consequential physics have not been explored in quantum phase transitions. Emergent symmetry of degenerate groundstates is discussed in possible connection to spontaneous symmetry breaking within the Landau theory. For a clear discussion, in this thesis, a quantum spin-1/2 plaquette chain system is considered. By mapping the quasi-one dimensional system into a one-dimensional system, we numerically investigate the quantum spin-1/2 Heisenberg-Ising dimer-plaquette chain with the Heisenberg intradimer and the Ising interdimer interactions in a magnetic field based on the infinite matrix product state representation of the wavefunction with the infinite time-evolving block decimation method. Phase boundary for nine different phases and degeneracy of groundstates in different phases are detected by the fidelity per lattice site between groundstates and an arbitrary reference states. From the local magnetizations and two-site correlations, an explicite expression of groundstates in different phases is obtained. For instance, it is found that a SU(2) global rotational symmetry, which is not included in the Hamiltonian symmetry group, is emerged in the singlet-dimerized phase. Also, the two degenerate groundstates found in seven of the nine phases are discussed in a spontaneous symmetry breaking picture with an emergent symmetry. As a cosequence, a quantum spin-1/2 plaquette chain system is shown to have rich emergent symmetry phenomena.