在此論文裡，我們主要討論三個主題。在此論文的第一部分，我們利用糾纏商與同
構於(0 +1)d共形場論代數結構的SU(1, 1)代數結構，研究了焠火玻色愛因斯坦凝聚系統與週期驅動偶合諧振子系統。我們發現糾纏熵在週期驅動偶合諧振子系統中能提供比聲子數更精準的相結構，而此刻畫也與量子態在龐加萊盤上的軌跡性質符合。另外，此研究也支持SU(1, 1)代數結構限制了加熱與非加熱相的刻畫。另一個工作則是與非厄米物理有關，我們在引入週期性邊界條件的SSH模型中加入一個具有宇稱和時間反演對稱的非厄米雜質，發現其糾纏熵與多體基態能量滿足非酉共形場論的預測，即其中心荷為c = −2，並且其能量為零的本徵態為例外點，我們也提供一些證據證明此例外點為造成負糾纏熵的原因。對於同樣的系統，我們也研究開放性與扭轉邊界條件，發現此負中心荷與邊界條件有極大的關聯，而此為非厄米系統對於邊界條件的強烈依賴性。接著，我們討論了非酉共形場論與酉共形場論的交界共形場論問題。相似於非厄米雜質，相同的例外點的穿透問題也導致了c = −2的糾纏熵。另外，這個酉與非酉交界共形場論也不符合酉交界共形場論的預測。

In this thesis, we mainly discuss three problems. In the first part of this thesis, we study the quenched Bose-Einstein condensates system and periodic-driven coupled oscillators system based on quantum entanglement and the SU(1,1) algebraic structure, which is isomorphic to the algebraic structure of (0+1) CFT. We observe that the quantum entanglement characterizes finer structure of the periodic-driven oscillating system which agrees with the trajectories on the Poincar'e disc. In addition to that, our study also supports the fact that the heating and the non-heating phase structures are confined by the SU(1,1) algebraic structure. In the second part of the thesis, we study PT-symmetric quantum impurity SSH model with exceptional points that exhibits c = -2 scaling using Cardy-Calabrese formula and the many-body ground state energy, agreeing with the prediction of the CFT. However, such results are sensitive to the boundary conditions even we fine-tuned the system to exceptional point under open boundary condition. In the last part of the thesis, we study the interface problem between SSH and non-Hermitian SSH model, and we give conjecture that explain the numerics based on the interface CFT and several lattice calculations. More, this unitary/non-unitary interface CFT doesn't agree with the predictions made by unitary interface CFT.