In this paper, I give an overview of some selected results in quantum many body theory, lying at the interface between mathematical quantum statistical mechanics and condensed matter theory. In particular, I discuss some recent results on the universality of transport coecients in lattice models of interacting electrons, with specic focus on the in- dependence of the quantum Hall conductivity from the electron-electron interaction. In this context, the exchange of ideas between mathematical and theoretical physics proved particu- larly fruitful, and helped in clarifying the role played by quantum conservation laws (Ward Identities), together with the decay properties of the Euclidean current-current correlation functions, on the interaction-independence of the conductivity.
Giuliani, A. (2020). ORDER, DISORDER AND PHASE TRANSITIONS IN QUANTUM MANY BODY SYSTEMS. RENDICONTI. CLASSE DI SCIENZE MATEMATICHE E NATURALI, 150, 73-116 [10.4081/scie.2016.576].
ORDER, DISORDER AND PHASE TRANSITIONS IN QUANTUM MANY BODY SYSTEMS
Giuliani, Alessandro
2020-01-01
Abstract
In this paper, I give an overview of some selected results in quantum many body theory, lying at the interface between mathematical quantum statistical mechanics and condensed matter theory. In particular, I discuss some recent results on the universality of transport coecients in lattice models of interacting electrons, with specic focus on the in- dependence of the quantum Hall conductivity from the electron-electron interaction. In this context, the exchange of ideas between mathematical and theoretical physics proved particu- larly fruitful, and helped in clarifying the role played by quantum conservation laws (Ward Identities), together with the decay properties of the Euclidean current-current correlation functions, on the interaction-independence of the conductivity.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
