Many-body localization in a one-dimensional system; Phase transitions in quantum many-body systems

Abstract

Most of closed many-body quantum systems can be thermalized on its own under a unitary time evolution. The properties of these systems are properly described by the principles of quantum statistical mechanics. However, in the presence of random disorders, a typical many-body system may undergo a phase transition from thermalization to localization. In the localized phase, the system cannot be thermalized even after long time evolution, and thus cannot be captured by quantum statistical mechanics. In this project, we numerically investigated the quantum phase transition between the thermalization and many-body localization in a one-dimensional spinless fermion chain. Considering the computational cost, we focused on fermion chains with adequate finite sizes, and applied the concept of parallel computing. The phase transition was examined from three aspects: the calculations of level statistic ratio, second Renyi entropy, and imbalance of fermion numbers. The three physical quantities had marked differences between the two phases. Consequently, by changing the disorder strength, we were able to observe the phase transition in the system.

Time crystal is a recent and hot topic in Condensed matter physics and Quantum Mechanics proposed by Nobel laureate Frank Wilczek. It is a unique structure that having repeat structure in not only space but also time. This unusual structure would break the discrete time translation symmetry and never reaches its thermal equilibrium. In this dissertation, we would demonstrate the properties of discrete time crystal by using a one-dimensional quantum Ising system. Each spin would have interacted in either nearest-neighbour interaction or long-range interaction. The simple spin driven mechanisms would flip the spin periodically and forming a discrete time crystal phase. We would investigate different system parameter such as system perturbation, the coupling force between spin in three-dimension and transverse magnetic field by using several effective analysis methods.