Introduction to Tensor Network Methods: Numerical simulations of low-dimensional many-body quantum systems

✍ Scribed by Simone Montangero

• Publisher: Springer International Publishing
• Year: 2018
• Tongue: English
• Leaves: 172
• Edition: 1st ed.
• Category: Library

✦ Synopsis

This volume of lecture notes briefly 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 numerical methods to tackle the quantum many-body problem: it reviews the numerical renormalization group and then focuses on tensor network methods, from basic concepts to gauge invariant ones. Finally, in the last part, the author presents some applications of tensor network methods to equilibrium and out-of-equilibrium correlated quantum matter.

The book can be used for a graduate computational physics course. After successfully completing such a course, a student 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.

✦ Table of Contents

Front Matter ....Pages i-xv
Introduction (Simone Montangero)....Pages 1-5
Front Matter ....Pages 7-7
Linear Algebra (Simone Montangero)....Pages 9-17
Numerical Calculus (Simone Montangero)....Pages 19-33
Front Matter ....Pages 35-35
Numerical Renormalization Group Methods (Simone Montangero)....Pages 37-47
Tensor Network Methods (Simone Montangero)....Pages 49-77
Symmetric Tensor Networks (Simone Montangero)....Pages 79-93
Front Matter ....Pages 95-95
Many-Body Quantum Systems at Equilibrium (Simone Montangero)....Pages 97-108
Out-of-Equilibrium Processes (Simone Montangero)....Pages 109-123
Back Matter ....Pages 125-172

✦ Subjects

Physics; Numerical and Computational Physics, Simulation; Quantum Physics; Quantum Computing; Mathematical Applications in the Physical Sciences