Skip to main content
SpringerLink
Log in

Introduction to Tensor Network Methods

Numerical simulations of low-dimensional many-body quantum systems

  • Book
  • © 2018

Overview

Authors:
  1. Simone Montangero

    1. Department of Physics and Astronomy “G. Galilei”, University of Padova, Padova, Italy

    View author publications

    You can also search for this author in PubMed   Google Scholar

  • Offers self-contained and course-tested lecture notes
  • Describes the study of lattice gauge theories via tensor network methods for the first time
  • Serves as a unique reference for computational physicists working in quantum science

This is a preview of subscription content, log in via an institution to check access.

Access this book

Log in via an institution
eBook USD 139.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book USD 179.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

Licence this eBook for your library

Institutional subscriptions

Table of contents (8 chapters)

  1. Front Matter

    Pages i-xv
    Download chapter PDF

  2. Introduction

    • Simone Montangero
    Pages 1-5

  3. The Single Body Problem

    1. Front Matter

      Pages 7-7
      Download chapter PDF

    2. Linear Algebra

      • Simone Montangero
      Pages 9-17

    3. Numerical Calculus

      • Simone Montangero
      Pages 19-33

  4. The Many-Body Problem

    1. Front Matter

      Pages 35-35
      Download chapter PDF

    2. Numerical Renormalization Group Methods

      • Simone Montangero
      Pages 37-47

    3. Tensor Network Methods

      • Simone Montangero
      Pages 49-77

    4. Symmetric Tensor Networks

      • Simone Montangero
      Pages 79-93

  5. Applications

    1. Front Matter

      Pages 95-95
      Download chapter PDF

    2. Many-Body Quantum Systems at Equilibrium

      • Simone Montangero
      Pages 97-108

    3. Out-of-Equilibrium Processes

      • Simone Montangero
      Pages 109-123

  6. Back Matter

    Pages 125-172
    Download chapter PDF
Back to top

Keywords

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. 

Authors and Affiliations

  • Department of Physics and Astronomy “G. Galilei”, University of Padova, Padova, Italy

    Simone Montangero

About the author

Simone Montangero received his Ph.D. in theoretical physics from the University of Milano and the Habilitation in theoretical physics from the University of Ulm. He is now leading the line of research on quantum science and technology at the Department of Physics and Astronomy of University of Padova, where he is Full Professor since 2017. He has been a Heisenberg Fellow of the German Science Foundation, a Humboldt Fellow and he is an IQOQI visiting fellow of the Institute for Quantum Optics and Quantum Information of the Austrian Academy of Science. He has pioneered the development of tensor network methods for quantum technologies and the application of optimal control theory to many-body quantum systems. He has been one of the principal actors in the development and application of tensor networks for lattice gauge theories. He has been involved in several national and European projects and is a member of the Science and Engineering Board of the Quantum Flagship. 


Bibliographic Information

Publish with us

Policies and ethics

Back to top

Search

Navigation