FASI QUANTISTICHE DELLA MATERIA
Anno accademico 2015/2016 - 1° anno - Curriculum FISICA DELLA MATERIACrediti: 6
SSD: FIS/02 - FISICA TEORICA, MODELLI E METODI MATEMATICI
Organizzazione didattica: 150 ore d'impegno totale, 102 di studio individuale, 48 di lezione frontale
Semestre: 2°
Prerequisiti richiesti
Fondamenti di meccanica statistica, Fondamenti di Fisica dei molti corpi, seconda quantizzazione.
Frequenza lezioni
Se concordato con gli studenti e/o in presenza di studenti stranieri, frequentanti nell’ambito di accordi Erasmus o di accordi quadro internazionali, il corso potra’ essere tenuto in lingua inglese.
Contenuti del corso
- Critical Phenomena.
Phase transitions, critical points, scaling, the role of dimensionality. The concepts of phase and symmetry. Conformal invariance. Landau Theory: symmetry breaking.
- Quantum Phase transitions.
The Ising model. Solidification transition. Transfer matrix formalism.
Correlation functions. The correspondence between statistical and quantum mechanics. The notion of a quantum phase transition.
- Impact of quantum phase transitions.
Example of quantum phase transitions and their relevance for modern quantum material science.Quantum technology.
- The quantum Ising model.
Transverse Ising Model in one-dimension: ground state, quantum critical point, duality argument, exact solution by Jordan-Wigner transformation.
- Quantum phase transition in systems of strongly interacting bosons.
The Bose-Hubbard model.Phase diagram. Physical realizations:Josephson junctions arrays, Cold atoms trapped in optical lattices.
- The quantum critical regime.
The effects of quantum criticality at finite temperature. Thermal crossover and quantum critical region. Thermal crossover in one dimensional Ising model in trasverse field.
- Topological matter.
Beyond Landau-symmetry breaking. Topological order. Topological quantum phase transitions in two spatial dimensions. Elements of lattice gauge theories. Topological order in one spatial dimension.
- Quantum phases of matter.
Entanglement in many-body systems. Short Vs long range entanglement in extended systems. Modern classification of quantum phases of matter.
Testi di riferimento
S. Sachdev, “Quantum Phase Transitions” (Cambridge University press 2011).
-X.G. Wen, “Quantum Field Theory of Many-body Systems: From the Origin of Sound to an Origin of Light and Electrons”, (Oxford University press 2007).