usc_2023

Material for the lectures at USC on 09/2023 The course involve 4 days, with 2 theory sessions each and one tutorial.

You will find

• the slides in the folder slides,
• the solved tutorials in the folder tutorials with solutions and
• the text of the tutorials in the folder tutorials

The material is not new but freely taken from my previous courses and the fantastic Glen Evenbly and Philippe Corboz tuotorials and materials that can be found here

For the tutorial I strongly suggest you use the ncon function, a simple function that allows to contract complex network, that you will find in the tuotrial folder

The schedule theory

• Day 1: Sessions:

  1. Introduction to tensors networks (1.5 hours)
  2. Entanglement (1 hour)

• Day 2: Sessions:

  1. Tensor contractions and decompositions (1.5 hours)
  2. Gauge freedom and gauge fixing (1 hour)

• Day 3: Sessions:

  1. Matrix product states (1.5 hours)
  2. Tensor Networks and stat-mech (1 hour)

• Day 4: Sessions:

  1. Variational optimization (1.5 hours)
  2. Time evolution and higher dimensions (1 hour)

  The schedule tutorials

• Day 1: Entropies of ground states

• Day 2: Tensor contractions

• Day 3: Stat mech with the corner transfer matrix

• Day 5: Ground states of 1D quantum systems