Quantum Renormalization of Berry Phase in the XY Heisenberg Model

Berry phase or geometric phase, is a phase difference acquired over the path of adiabatic processes, which comes from the geometrical properties of the parameter space of the system. In this paper, we apply the quantum renormalization group (QRG) theory on one dimensional spin-1/2 XY Heisenberg chain. Using the recursion relations of the QRG, we calculate the renormalized Berry phase of the ground state of a three spin block. We show that the discontinuity of the Berry phase marks the quantum phase transition (QPT) in this model. Plots of the Berry phase in terms of the anisotropy parameter at different steps of the QRG cross each other at the critical point of the model. Also, the critical exponent of the correlation length is obtained by studying the scaling behavior of the derivative of the Berry phase near the critical point.