1 / 14

Entanglement Renormalization

Frontiers in Quantum Nanoscience A Sir Mark Oliphant & PITP Conference. Entanglement Renormalization. Noosa, January 2006. Guifre Vidal The University of Queensland. Science and Technology of. quantum many-body systems. simulation algorithms. entanglement.

deanna
Download Presentation

Entanglement Renormalization

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. Frontiers in Quantum Nanoscience A Sir Mark Oliphant & PITP Conference Entanglement Renormalization Noosa, January 2006 Guifre Vidal The University of Queensland

  2. Science and Technology of quantum many-body systems simulation algorithms entanglement Computational Physics Quantum Information Theory Introduction

  3. Outline • Overview: new simulation algorithms for quantum systems • Time evolution in 1D quantum lattices (e.g. spin chains) • Entanglement renormalization

  4. 2D 2005 1D Entanglement renormalization PEPS • Verstraete • Cirac 2004 2D TEBD 2003 time evolution ground state 1D 1D DMRG • White 1992 Recent results • Hastings • Osborne time (Other tools: mean field, density functional theory, quantum Monte Carlo, positive-P representation...)

  5. N = 100 dim(H) = Computational problem • Simulating N quantum systems on a classical computer seems to be hard Hilbert Space dimension = 16 2 4 8 “small” system to test 2D Heisenberg model (High-T superconductivity) Hilbert Space dimension = 1,267,650,600,228,229,401,496,703,205,376

  6. problems: solutions: (i) state • Use a tensor network: coefficients (for 1D systems MPS, DMRG) i1 ... in i1 ... in i1 in … (ii) evolution • Decompose it into small gates: (if , with ) coefficients i1 ... in i1 in … jn j1 … j1 ... jn

  7. efficient description of and Trotter expansion matrix product state i1 ... in • efficient update of i1 ... in = operations j1 ... jn simulation of time evolution in 1D quantum lattices (spin chains, fermions, bosons,...)

  8. tensor network (1D: matrix product state) i1 in … i1 in … coefficients coefficients coef efficiency entanglement A B Entanglement & efficient simulations • Schmidt decomposition

  9. number of shared singlets A:B Entanglement in 1D systems • Toy model I (non-critical chain): correlation length • Toy model II (critical chain):

  10. arbitrary state spins coefficients • non-critical 1D coefficients spins • critical 1D spins coefficients change of attitude summary: In DMRG, TEBD & PEPS, the amount of entanglement determines the efficiency of the simulation Entanglement renormalization disentangle the system

  11. Entanglement renormalization no disentanglement partial disentanglement Examples: complete disentanglement

  12. Entanglement renormalization Multi-scale entanglement renormalization ansatz (MERA)

  13. C, fortran, highly optimized days in “big” machine a few hours in this laptop matlab Performance: system size (1D) time code memory greatest achievements in 13 years according to S. White DMRG ( ) Entanglement renormalization ( ) first tests at UQ Extension to 2D: work in progress

  14. Understanding the structure of entanglement in • quantum many-body systems is the key to achieving • an efficient simulation in a wide range of problems. or simply... • There are new tools to efficiently simulate quantum • lattice systems in 1D, 2D, ... Conclusions

More Related