Interaction-induced Monopole-stretching and Finite Temperature Generalization of the Chern Number

Motivated by the experimental realization of probing the Chern number of superconducting qubits, this work studies the finite temperature generalization of the Chern number of two-components Bose spinors with on-site interaction. We study the topological properties of interacting Bose spinors, and generalize the concept of Chern number to the finite temperature regime. It is found that the mixed Chern number of the one-particle reduced density matrix is directly related to the visibility of the mixed geometric phase. This result holds for any two-components Bose spinors. Finally, we propose an interacting two-components Bose spinor with time-reversal symmetry, where the visibility could be measured, and the dynamical phase could be canceled, to directly extract the monopole charge. Our work paves the way for experimental validation of theoretical predictions regarding topological phenomena in quantum systems.