Basic Training in Condensed Matter Physics

BASIC TRAINING IN CONDENSED MATTER PHYSICS

Physics 7654, Spring 2024 Jim Sethna, Jane Wang, Tomás Arias, and Erich Mueller Wednesdays and Fridays, 2:30-4:00, PSB 120 sethna.lassp.cornell.edu/Teaching/BasicTraining/

Jan 24 - Feb 16	Feb 21 - Mar 1	Mar 13 - Apr 12	Apr 17 - May 10
Jim Sethna	Jane Wang	Tomás Arias	Erich Mueller
Why does science work? Information geometry, multiparameter models, and the emergence of simplicity	Physics of Life	The Theory of Density Functional Theories, Electronic and Classical: From N- and V- representability theorems through convexity to excited states and statistical mechanics	Practical introduction to matrix product states and the density matrix renormalization group

WHAT IS BASIC TRAINING?

Cornell has a diverse group of condensed matter theorists, studying topics ranging from cold atoms to topological quantum systems to Sudoku algorithms. This course is a venue for sharing that breadth: to give condensed matter theory students broad exposure to the tools/techniques/topics of the various research groups. The title "Basic Training in Condensed Matter Physics" reflects the importance our theory group places on the course. Some topics are indeed "basic" and approachable by first year graduate students in physics or related disciplines. Others are "advanced topics" which more senior students will get more out of. We encourage theorists and experimentalists from all departments to attend, and LASSP theory grads all to attend. To take the course for credit, complete two of the four modules (including the homework).

TOPICS SPRING 2024

Jim Sethna Why does science work? Information geometry, multiparameter models, and the emergence of simplicity Complex models in physics, biology, economics, and engineering are usually successful because their microscopic details are not crucial for describing the real world. We explain their success using information geometry, combining differential geometry with approximation theory to understand the reason simplicity emerges from complex underpinnings. Web site

Jane Wang Physics of Life We will start with a brief history of physicists' contributions to our understanding of life, and will survey recent research at the interface between physics and biology, illustrated with works done here at Cornell and elsewhere.

Tomás Arias The Theory of Density Functional Theories, Electronic and Classical: From N- and V- representability theorems through convexity to excited states and statistical mechanics Density Functional Theory, as recognized by Walter Kohn's share of the Nobel prize in 1998, with its radical simplification of electronic structure theory, has become one of the most important tools in materials physics and chemistry. This module will emphasize the theoretical underpinnings of Density Function Theory in these various contexts, looking at the underlying theorems, some of the thorny mathematical issues (such as N- and v- representability), the extensions to finite temperature, multicomponent, and excited states. Time permitting, we will also discuss how the same sort of simplification is possible for the theory of the equilibrium molecular structure of liquids and to electronic systems in equilibrium with such liquids.

Erich Mueller Practical introduction to matrix product states and the density matrix renormalization group The Density Matrix Renormalization Group (DMRG) and related tensor-network methods have become the workhouse numerical tools for studying one dimensional (1D) quantum many-body problems. For certain classes of problems these approaches yield unbiased "numerically exact" results. In this module you will learn the theory behind the method — which involves developing clever ways of writing and manipulating wavefunctions. You will write a DMRG code from scratch, and use it to investigate a quantum phase transition. Finally you will learn how to use some of the tensor-network codes which are readily available.
Despite the impressive sounding jargon (density matrices, renormalization group, and tensor networks) the module should be accessible to any student with a good undergraduate-level understanding of quantum mechanics and linear algebra. The language of tensor networks has become pervasive, and even students who have less interest in numerical methods should find the module useful and illuminating.