Seminari del Dipartimento
Fisica Matematica Adiabatic currents for interacting electrons on a lattice D. Monaco 21-11-2017 - 14:30 Largo San Leonardo Murialdo,1 - Pal.C - AULA 311
Consider a system of interacting fermions on a finite lattice modelled by a gapped many-body Hamiltonian H(t), depending adiabatically on time. I will present an adiabatic theorem for the trace per unit volume of local observables in a state evolving adiabatically from a ground state of H(0). The theorem holds with error estimates that are uniform in the size of the system. Our result provides an adiabatic expansion to all orders, in particular, also for initial data that lie in eigenspaces of degenerate eigenvalues. The adiabatic theorem allows to compute the current density induced by the adiabatic change of the Hamiltonian, and derive rigorously the so-called linear response formula for a system of interacting fermions in a ground state, with error estimates uniform in the system size. I will also discuss the application to quantum Hall systems. This is based on joint work with Stefan Teufel. |