General Prerequisites:
Although the lectures will be self-contained, this course is designed as a follow-on to Quantum Matter I. Familiarity with ideas introduced in Advanced Quantum Theory and Renormalization Group will be useful but not essential.
Course Term: Trinity
Course Lecture Information: 20 lectures
Course Overview:
Lecturer: Prof. S.A. Parameswaran
Credits: 1.25 units (20 lectures)
Assessment: Homework Completion
Credits: 1.25 units (20 lectures)
Assessment: Homework Completion
Learning Outcomes:
Course Synopsis:
Syllabus: Modern condensed matter physics is increasingly focused on understanding the properties of strongly interacting systems. Traditional techniques that rely on diagrammatic perturbation theory about the independent electron approximation are often insufficient to provide an adequate description of the rich phenomena possible in this setting. Instead, their study requires a variety of ideas often also invoked in the study of quantum field theories in the non-perturbative regime. This course will cover some of the major themes in the study of correlated systems, including applications of the renormalization group to interacting Fermi systems, bosonization, superfluid-Mott insulator transitions, and competing orders.
Rough Plan of Topics and Lectures
- Renormalization group for Interacting Fermions: momentum-shell RG for φ4 theory; RG and the Fermi surface; BCS and CDW as competing instabilities; RG in d=1 and emergence of Luttinger liquids
- Bosonization: Fermion-boson dictionary; application to spinless fermions; sine-Gordon model and Kosterlitz-Thouless flow; emergence of insulators from commensuration
- Competing Orders: Bose-Hubbard model and Superfluid-Mott transition; duality; commensurability and “Lieb-Schulz-Mattis” constraints; Landau-forbidden phases and transitions in the Bose-Hubbard model
Course Book: No single textbook, but useful books include Quantum Field Theory in Condensed Matter by R. Shankar (Cambridge University Press, 2017); Quantum Phase Transitions by S. Sachdev (Cambridge University Press, 2011); and Quantum Physics in One Dimension by T. Giamarchi (Oxford University Press, 2003). Will be supplemented by lecture notes.
Rough Plan of Topics and Lectures
- Renormalization group for Interacting Fermions: momentum-shell RG for φ4 theory; RG and the Fermi surface; BCS and CDW as competing instabilities; RG in d=1 and emergence of Luttinger liquids
- Bosonization: Fermion-boson dictionary; application to spinless fermions; sine-Gordon model and Kosterlitz-Thouless flow; emergence of insulators from commensuration
- Competing Orders: Bose-Hubbard model and Superfluid-Mott transition; duality; commensurability and “Lieb-Schulz-Mattis” constraints; Landau-forbidden phases and transitions in the Bose-Hubbard model
Course Book: No single textbook, but useful books include Quantum Field Theory in Condensed Matter by R. Shankar (Cambridge University Press, 2017); Quantum Phase Transitions by S. Sachdev (Cambridge University Press, 2011); and Quantum Physics in One Dimension by T. Giamarchi (Oxford University Press, 2003). Will be supplemented by lecture notes.