Exploring Some Fundamental Problems in Quantum Phase Transitions from the Perspectives of Quantum Information Science.

摘要

Quantum phase transitions (QPTs) refer to an abrupt change in the ground state wavefunction at absolute zero temperature when tuning some external non-thermal parameters. Though much effort has been devoted to study QPTs in the past, our understanding on the subject is still far from complete. In this thesis, we used concepts from quantum information science, namely the quantum entanglement and the quantum fidelity, to explore some of the open questions in the field.;The first issue we investigated is on how to characterize the nature of a quantum phase. Two schemes have been proposed. The first one is the fidelity spectrum. Physically, it tells us the scattering amplitudes of an incident ground state wavefunction into different eigenstates of the Hamiltonian at a different value of the driving parameter. The fidelity spectrum is studied in two correlated spin systems, namely the one-dimensional (1D) transverse-field Ising model and the two-dimensional (2D) Kitaev model on a honeycomb lattice. We found that the spectrum exhibits qualitative different behaviors in different phases of the models. From the distribution of it, one can also determine the dominating k modes in a phase.;The other scheme proposed is to investigate the spectrum of the reduced density matrix that is used to calculate the entanglement and construct the potential order parameter from it. We have applied the scheme on the 1D Hubbard and extended Hubbard model. By investigating the one-site and two-site reduced density matrix spectrum respectively, the order parameter for the spin-density wave (SDW), charge-density wave (CDW), phase separation (PS), and the bond-order wave (BOW) phase of the models are constructed systematically.;The second issue we studied is the capability of the fidelity susceptibility to detect a Berezinsky-Kosterlitz-Thouless (BKT) transition. In particular, the fidelity susceptibility (FS) in the 1D Hubbard model and the extended Hubbard model is calculated using density-matrix renormalization group technique. We found that the fidelity susceptibility diverges at some distance away from the BKT transition point of the models.