Introduction to Tensor Network Methods

This volume of lecture notes first introduces the basic concepts needed in any computational physics course: software and hardware, programming skills, linear algebra and differential calculus. It then presents more advanced concepts, providing the knowledge that every computational physicist should possess in order to tackle the quantum many-body problem. Although other successful approaches are also briefly covered, this part of the book focuses on tensor network methods. Finally, in the last part, the author introduces elements of group theory and discusses the consequences of symmetries in the correlated quantum world and tensor networks. The book can be used for upper undergraduate computational physics courses, or split into a Bachelor (first part) and a Master or Ph.D. course (last part). After following this program, students should be able to write a tensor network program and can begin to explore the physics of many-body quantum systems. The book can also serve as a reference for researchers working or starting out in the field.