The example of strongly correlated electron systems from the perspective of high energy physics

In this thesis, we give three examples of applying high energy physics method or idea in strongly correlated electron system. The first one is considering a curved space-time hydrodynamics theory for twisted bilayer graphene (TBG) and rotating bilayer graphene (RBG).We have predicted the possible quantized Thouless pumping in RBG for low driven frequency as a new kind of floquet engineering. In the second example, we study the C=2 fractioanl Chern insulator (FCI) candidate in twisted bilayer checkboard lattice (TBCB). We interpret the quasi-hole counting in particle entanglement spectrum (PES) based on SU(2) Halperin spin singlet ansatz and generalized Pauli principle, which is similar to the SU© color singlet in high energy physics. Finally, we investigate the general ab-initio method for crystalline material based on quasi-classical U(1) lattice gauge theory (or QED based ab-initio). We design a simpler algorithm for fixing U(1) gauge when implementing Monte-Carlo sampling without introducing ghost field.