Introduction to Tensor Network Methods

Numerical simulations of low-dimensional many-body quantum systems

  • Simone Montangero

Table of contents

  1. Front Matter
    Pages i-xv
  2. Simone Montangero
    Pages 1-5
  3. The Single Body Problem

    1. Front Matter
      Pages 7-7
    2. Simone Montangero
      Pages 9-17
    3. Simone Montangero
      Pages 19-33
  4. The Many-Body Problem

    1. Front Matter
      Pages 35-35
    2. Simone Montangero
      Pages 37-47
    3. Simone Montangero
      Pages 49-77
    4. Simone Montangero
      Pages 79-93
  5. Applications

    1. Front Matter
      Pages 95-95
    2. Simone Montangero
      Pages 97-108
    3. Simone Montangero
      Pages 109-123
  6. Back Matter
    Pages 125-172

About this book


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. 


computational quantum physics textbook tensor network methods lattice gauge theories simulations numerical simulations in quantum mechanics quantum many-body problem matrix diagonalization quantum phase transitions global symmetries

Authors and affiliations

  • Simone Montangero
    • 1
  1. 1.Department of Physics and Astronomy “G. Galilei”University of PadovaPadovaItaly

Bibliographic information

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