https://quantumghent.github.io/TensorTutorials/

Tutorial outline

I. Prerequisites

1. General Introduction
   • who is who?
   • practicalities during the year
   • Julia
   • Git(Hub)
2. Introduction to Quantum Many-Body theory
   • context, history, purpose, relevance
   • second quantization
   • tensor product
   • quantum <-> classical
3. Tensor Networks
   • context, history, purpose, relevance
   • multi-linear algebra
   • graphical notation
   • computational complexity
4. Symmetries
   • group theory
   • fermions
   • fusion categories

II. Matrix Product States

1. Matrix Product States
   • MPS as a polynomial Ansatz
   • entanglement and area laws
   • gauge freedom
   • expectation values
   • correlators
2. Matrix Product Operators
   • Statistical mechanics as an MPO
   • Jordan-block form of MPO
   • expectation values
3. Infinite Matrix Product States
   • gauging revisited
   • expectation values
   • structure factors
4. Basic Algorithms
   • Simple Update
   • Trotterization
   • TEBD
5. Applications
   • Transverse-Field Ising Model
   • Classical Ising Model

III. Tensor Network Algorithms

1. Fixedpoint Algorithms
   • DMRG
   • VUMPS
   • Krylov methods
2. Time-Evolution Algorithms
   • TDVP
   • MPO Compression
   • Finite Temperature
3. Excitations
   • Finite Excitations
   • Quasiparticle ansatz
4. Gradient Methods
   • Quasi-Newton methods
   • Grassmann optimization
   • AD
5. PEPS
6. Dynamic Bonddimensions
   • Multi-Site Algorithms
   • MPS Truncation
   • MPO-MPS approximation

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Local development:

Run the build.sh script to build the pages locally. Optionally, you can pass the -d flag to update the dependencies.

./build.sh [-d]