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This course explores computational approaches for quantum many-body systems, covering topics such as spin systems, entanglement, tensor networks, and variational approaches. Learn the fundamentals and gain practical skills through programming exercises.

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## Computational approaches for quantum many-body systems

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**Computational approaches for quantum many-body systems**HGSFP Graduate Days SS2019 Martin Gärttner**Why programming exercises?**What I cannot create I do not understand. [Richard Feynman]**Course overview**Lecture 1: Introduction to many-body spin systems Quantum Isingmodel,Bloch sphere, tensor structure, exact diagonalization Lecture 2: Collective spin models LMG model, symmetry, semi-classical methods,Monte Carlo Lecture 3: Entanglement Mixed states, partial trace, Schmidt decomposition Lecture 4: Tensor network states Area laws, matrix product states,tensor contraction, AKLT model Lecture 5: DMRG and other variational approaches Energy minimization, PEPS and MERA, neural quantum states**Learning goals**After today you will be able to … • … explain how collective spins map to two-mode bosonic models. • … derive mean field equations for spin models. • … apply the semi-classical truncated Wigner method to simulate the dynamics of collective spins.**References**• Lecture notes Anatoli Polkovnikov: http://physics.bu.edu/~asp/teaching/lecture_notes_wigner_boulder_2013.pdf • A. Polkovnikov. Ann. Phys., 325:1790, 2010. https://arxiv.org/abs/0905.3384

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