  Recently, dynamical anomalies more than critical slowing down are often
observed near both the continuous and first-order phase transition points. We
propose that the universal anomalies could originate from the geometric phase
effects. A Pancharatnam-Berry phase is accumulated continuously in quantum
states with the variation of tuning parameters. Phase transitions are supposed
to induce a abrupt shift of the geometric phase. In our multi-level quantum
model, the quantum interference induced by the geometric phase could prolong or
shorten the relaxation times of excited states at phase transition points,
which agrees with the experiments, models under sudden quenches and our
semi-classical model. Furthermore, we find that by setting a phase shift of
\text{\ensuremath{\pi}}, the excited state could be decoupled from the ground
state by quantum cancellation so that the relaxation time even could diverge to
infinity. Our work introduces the geometric phase to the study of conventional
phase transitions and quantum phase transition, and could substantially extend
the dephasing time of qubits for quantum computing.
