A toy model for quantum glasses and quantum optimization problems

by Prof. Francesco Zamponi (Laboratoire de Physique Théorique, Ecole Normale Supérieure, Paris)

Wednesday 20 Apr 2011, 14:00 → 16:00 Europe/Rome

Aula Rasetti (Dip. di Fisica - Edificio G. Marconi)

The interplay of disorder, frustration and quantum fluctuations is relevant for many problems, from quantum glasses to quantum algorithms, and is related to the problem of many-body localization. I will discuss the quantum version of a simplified model of optimization problems, where quantum fluctuations are introduced by a transverse field acting on the qubits. I will show that the quantum Hamiltonian has a complex low-energy spectrum, characterized by an abrupt condensation transition and a continuum of level crossings as a function ! of the transverse field. I will show that this complex structure has deep consequences for the behavior of quantum algorithms attempting to find solutions to these problems. Moreover, I will show that this structure implies that quantum fluctuations promote glassiness in hard sphere models.