QUANTUM PHASES OF MATTER

Academic Year 2015/2016 - 1° Year - Curriculum FISICA DELLA MATERIA
Teaching Staff: Luigi AMICO
Credit Value: 6
Scientific field: FIS/02 - Theoretical physics, mathematical models and methods
Taught classes: 48 hours
Term / Semester:

Detailed Course Content

  • 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.


Textbook Information

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).