物理系学术报告 Physics Department Seminar
Fidelity susceptibility, quantum adiabatic condition, and quantum phase transitions
In this talk, I will firstly introduce the quantum fidelity approach to quantum phase transitions based on its leading term, i.e. the fidelity susceptibility. The fidelity susceptibility denotes the adiabatic leading response of the ground state to the driving parameter. Differ from traditionally approach based on the ground-state energy, the fidelity susceptibility shows distinct scaling and singular behaviours around the critical point.
Secondly, I would like to introduce the relation between the fidelity susceptibility and quantum adiabatic theorem. For a d-dimensional quantum many-body system, we show that the duration time required by its ground-state adiabatic process does not depend on the microscopic details, but the quantum adiabatic dimension, which for instance in the gapless region, depends on global properties like dimensionality, the dynamic exponent, and the scaling dimension of the driving Hamiltonian. The quantum adiabatic theorem might be violated in case that the quantum adiabatic dimension is larger than the system's real dimension.