1 / 10

Computational approaches for quantum many-body systems

Learn about computational methods for quantum many-body systems in this course. Topics include quantum Ising model, tensor structure, Monte Carlo methods, entanglement, tensor network states, and more.

jlocke
Télécharger la présentation

Computational approaches for quantum many-body systems

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Computational approaches for quantum many-body systems HGSFP Graduate Days SS2019 Martin Gärttner

  2. 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

  3. Learning goals After today you will be able to … • … explain the matrixproduct state ansatz. • … translate between tensors and their diagrammatic representation. • … derive that the bond dimension bounds the Schmidt rank. • … evaluate observables for MPS, especially with periodic boundaries.

  4. Unreasonably large Hilbert space Hilbert space: Physical corner Martin Gärttner - BDC 2018

  5. Unreasonably large Hilbert space Physical states: Can be reached through local Hamiltonians in polynomial time. Ground states of local gapped Hamiltonians. Locally entangled. Area law states Martin Gärttner - BDC 2018

  6. Area law vs. volume law volume law area law Ground states of local gapped Hamiltonians Only k-body terms, k~1 Excitation gap does not go to zero as Area law → half-chain entropy doesn’t grow with system size 1D

  7. Representing quantum states: MPS • Consider N spins in 1D parameters

  8. Representing quantum states: MPS . . . • Consider N spins in 1D . . .

  9. Representing quantum states: MPS A B • Consider N spins in 1D parameters parameters • Finite entanglement capacity:

  10. References Roman Orus: A practical introduction to tensor networks Very nice tutorial! AKLT model: English Wikipedia Original AKLT paper: Phys. Rev. Lett. 59, 799 (1987)

More Related