Quantum Phase Transitions and Dynamics in Strongly Correlated Systems: An Infinite Matrix Product State Approach

Abstract

This thesis explores non-equilibrium phenomena in strongly correlated quantum systems, focusing on the half-filled one-dimensional Hubbard model at zero temperature in the thermodynamic limit. Using tensor network methods, particularly infinite matrix product states (iMPS), we simulate the real-time dynamics induced by optical pump pulses. A laser pulse is modeled by a time-dependent vector potential applied via the Peierls substitution, with dynamics computed using the infinite time-evolving block decimation (iTEBD) algorithm. We investigate the emergence of a superconducting-like eta-pairing state with off-diagonal long-range order (ODLRO) and confirm that eta-pairing correlations are significantly enhanced for certain pulse parameters. Additionally, signatures of dynamical quantum phase transitions (DQPTs) are observed in the Loschmidt echo rate function. Finite-entanglement scaling is employed to extract the central charge and analyze criticality of the ground state.