SNU-CTP Distinguished Lecture Series on "Tensor networks: from basics to tangent space methods"

Lecture notes & videos

The references mentioned during lectures are listed in this .bib file.

By now, the uploaded videos are raw versions that have not yet been post-processed. We will (i) split the videos into subsections and (ii) try to remove the echoes in the recordings of Lecture 1.

1. Tensor network basics (note_gapped) (note_full) (video_playlist)
   (The videos from this lecture contain echoes, which we couldn't remove. If you know how to remove them, please feel free to contact us.)

   • [TNB.1] Why matrix product states? (video)

   • [TNB.2] Arrow conventions (video)

   • [TNB.3] Tensor network diagrams (video)

   • [TNB.4] Unitaries and isometries (video)

   • [TNB.5] Singular value decomposition (SVD) (video)

   • [TNB.6] Schmidt decomposition (video)

2. Matrix product states (MPSs) (note_gapped) (note_full) (video_playlist)

   • [MPS.1] Reshaping a generic tensor into an MPS form (video)

   • [MPS.2] MPS overlaps (video)

   • [MPS.3] Left- and right-normalized MPSs (video)

   • [MPS.4] Various canonical MPS forms (video)

   • [MPS.5] Applying MPO to a mixed-canonical state (video)

3. Density-matrix renormalization group (DMRG) (note_gapped) (note_full) (video_playlist)

   • [DMRG.1] Iterative ground state search (video)

   • [DMRG.2] Lanczos method (video)

   • [DMRG.3] Two-site update (video)

4. Tangent space (note_gapped) (note_full) (video_part1) (video_playlist)

   • [TS.1] Motivation: why is tangent space useful? (video)

   • [TS.2] MPS canonical forms (video)

   • [TS.3] Kept and discarded spaces (video)

   • [TS.4] Kept and discarded projectors (video)

   • [TS.5] Tangent space projector (video)

5. Time evolution: time-dependent variational principle (TDVP) (note_gapped) (note_full) (video_playlist)

   • [TDVP.1] One-site TDVP (video)

   • [TDVP.2] Two-site projectors (video)

   • [TDVP.3] Two-site TDVP (video)

6. Controlled bond expansion (CBE) (note_gapped) (note_full) (video_playlist)

   • [CBE.1] Energy variance (video)

   • [CBE.2] CBE for DMRG (video)

   • [CBE.3] Shrewd selection (video)

   • [CBE.4] CBE-TDVP (video)

   • [CBE.5] CBE + mixing (video)

7. Dynamical correlators
   We don't publish the lecture notes and the video recordings of this lecture, since it contains unpublished results.