Berry phases in superconducting transitions

TL;DR

This paper extends the concept of Berry phases to superconducting transitions, revealing how geometric phases can detect phase boundaries and spin gaps in many-body systems with fractional particles per site.

Contribution

It generalizes Berry phases to cases where the ground state evolves into an excited state after one cycle, enabling detection of superconducting phase transitions in complex systems.

Findings

Berry phases jump by pi at superconducting phase boundaries

Transitions in the extended Hubbard chain match Bethe ansatz results

Spin Berry phase jumps when a spin gap opens

Abstract

I generalize the concept of Berry's geometrical phase for quasicyclic Hamiltonians to the case in which the ground state evolves adiabatically to an excited state after one cycle, but returns to the ground state after an integer number of cycles. This allows to extend the charge Berry phase gamma_c related to the macroscopic polarization, to many-body systems with fractional number of particles per site. Under certain conditions, gamma_c and the spin Berry phase gamma_s jump in pi at the boundary of superconducting phases. In the extended Hubbard chain with on-site attraction U and nearest-neighbor interaction V at quarter filling, the transitions detected agree very well with exact results in two limits solved by the Bethe ansatz, and with previous numerical studies. In chains with spin SU(2) symmetry, gamma_s jumps when a spin gap opens.