Les Houches lecture notes on tensor networks

2025/12/30 by Bram Vancraeynest-De Cuiper, Weronika Wiesiolek, Frank Verstraete · 3 voices
Physics and Astronomy · Computer Science · #Quantum many-body systems #Topological Materials and Phenomena #Quantum Information and Cryptography

paper · pdf · doi:10.21468/scipostphyslectnotes.128

Abstract

Tensor networks provide a powerful new framework for classifying and simulating correlated and topological phases of quantum matter. Their central premise is that strongly correlated matter can best be understood by studying the underlying entanglement structure and its associated (generalised) symmetries. In essence, tensor networks provide a compressed, holographic description of the complicated vacuum fluctuations in strongly correlated systems, and as such they break down the infamous many-body exponential wall. These lecture notes provide a concise overview of the most important conceptual, computational and mathematical aspects of this theory.

Citations

• The bond-algebraic approach to dualities
• Matrix product states, projected entangled pair states, and variational renormalization group methods for quantum spin systems
• The density-matrix renormalization group in the age of matrix product states
• Fault-tolerant quantum computation by anyons
• Two soluble models of an antiferromagnetic chain
• Anyons in an exactly solved model and beyond

Discussions

• Although 2025 was absolutely shocking in terms of the cruelty of powerful people, science can still be a refuge from it. A highlight for me was retreating to the mountains to teach at the Les Houches [bsky, 39 points, 0 comments]
• According to these Les Houches lecture notes (page 12), it is possible to find an injective, bond dimension 2 MPO representation of the exponential of the quantum Ising Hamiltonian (with no external f [stackexchange, 2 points]
• Frank's Les Houches lecture is on arXiv! arxiv.org/abs/2512.24390 [bsky, 1 points, 0 comments]

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