INVARIANT TENSORS AS A MACROSCOPIC MEMORY OF MICROSCOPIC STRUCTURE

N. E. GRANDI

La Plata / Buenos Aires

Workshop; Ten Years of the Strings@ar Network workshop; 2013

Red Strings@ar

Based on a detailed symmetry analysis, we state the general rules to build up the effective low energy field theory describing a system of electrons weakly interacting with the lattice degrees of freedom. The basic elements in our construction are what we call the "memory tensors", that keep track of the microscopic discrete symmetries into the coarse-grained action. The present approach can be applied to lattice systems in arbitrary dimensions and in a systematic way to any desired order in derivatives. We apply the method to the honeycomb lattice and re-obtain the by now well-known effective action of Dirac fermions coupled to fictitious gauge fields. As a second example, we derive the effective action for electrons in the kagom´e lattice, where our approach allows to obtain in a simple way the low energy electron-phonon coupling terms.