Algorithm of Tensor Network representations
This course provide an comprehensible introduction to two pivotal tensor network states—the Matrix Product States (MPS) and the Projected Entangled Pair States (PEPS)—for simulating complex quantum systems in condensed matter physics. First originated from the density matrix renormalization group (DMRG) method, the MPS excels at modeling one-dimensional (1D) systems by efficiently representing ground states, excited states, and dynamics through low-rank tensor decomposition. Its computational tractability makes it ideal for studying spin chains, quantum phase transitions, and critical phenomena in 1D lattices.
PEPS extends these principles to two-dimensional (2D) and higher-dimensional systems, capturing intricate entanglement structures that evade traditional methods. PEPS utilizes tensor networks to simulate statistical models, topological order, quantum spin liquids, and anyonic excitations in high-dimensional lattices. However, PEPS also brings higher computational complexity to the algorithm and provides greater challenges to algorithm design.
PEPS extends these principles to two-dimensional (2D) and higher-dimensional systems, capturing intricate entanglement structures that evade traditional methods. PEPS utilizes tensor networks to simulate statistical models, topological order, quantum spin liquids, and anyonic excitations in high-dimensional lattices. However, PEPS also brings higher computational complexity to the algorithm and provides greater challenges to algorithm design.
Lecturer
Date
16th October, 2026 ~ 8th January, 2027
Location
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| Friday | 10:40 - 15:05 | Shuangqing | ZOOM 06 | 537 192 5549 | BIMSA |
Prerequisite
Quantum Mechanics
Syllabus
After quickly supplementing the preliminary knowledge, we will introduce several representative tensor network algorithms of MPS and PEPS, such as DMRG, TEBD, TDVP, etc., and for the PEPS algorithms, we will talk about TRG, HOTRG, SRG, Loop-TNR, CTMRG, AutoDifferentiation, etc.
Reference
Orus, R. Annals of Physics 349, 117–158 (2014).
Orus, R. The European Physical Journal B 87, (2014).
Schollwoeck, U. Annals of Physics 326, 96–192 (2011).
Verstraete, F., Cirac, J. I. & Murg, V. Advances in Physics 57, 143–224 (2008).
Orus, R. The European Physical Journal B 87, (2014).
Schollwoeck, U. Annals of Physics 326, 96–192 (2011).
Verstraete, F., Cirac, J. I. & Murg, V. Advances in Physics 57, 143–224 (2008).
Audience
Undergraduate
, Advanced Undergraduate
, Graduate
, Postdoc
Video Public
Yes
Notes Public
No
Language
Chinese
Lecturer Intro
Song Cheng is an Associate Professor at the Yanqi Lake Beijing Institute of Mathematical Sciences and Applications (BIMSA). He holds a PhD in theoretical physics from the Institute of Physics, CAS, and previously served as an Assistant Professor at the Center of Quantum Computing in Pengcheng Laboratory. His current research focuses on investigating the relationship between machine learning, quantum many-body physics, and quantum computing through tensor networks.