Berry Phase in Quantum Field Theory: Diabolical Points and Boundary Phenomena

Understand

We study aspects of Berry phase in gapped many-body quantum systems by means of effective field theory.

• Once the parameters are promoted to spacetime-dependent background fields, such adiabatic phases are described by Wess-Zumino-Witten (WZW) and similar terms.
• In the presence of symmetries, there are also quantized invariants capturing generalized Thouless pumps.
• Consideration of these terms provides constraints on the phase diagram of many-body systems, implying the existence of gapless points in the phase diagram which are stable for topological reasons.