Rakov M. Numerical simulation of quantum many body systems using tensor networks

The thesis is devoted to a study of entanglement properties and phase structure of the quantum spin-1/2 XXZ model and the spin-1 bilinear-biquadratic Heisenberg (BBH) model with quadratic Zeeman effect. The boundaries of the dimerized phase at the biquadratic point was determined, and it was proved that the nematic phase can exist only in a narrow region of the control parameter in the vicinity of SU(3)-symmetric point for the model without anisotropy. It was shown that the entanglement structure of the excited states of the XXZ model cannot be described satisfactorily by one- and two-site entanglement measures in the ferromagnetic phase. During the work, the numerical method that uses matrix product states (MPS) for periodic boundary conditions (PBC) was improved by using U(1)- and SU(2)-symmetric MPS as variational states (according to the Mermin-Wagner theorem).