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MERA in 2D ( Multi-scale Entanglement Renormalization Ansatz )

MERA in 2D ( Multi-scale Entanglement Renormalization Ansatz ). Łukasz Cincio ( POSTER ) Jacek Dziarmaga Marek M. Rams ( POSTER ) @ Uniwersytet Jagielloński. arXiv:0710.3829 accepted in Phys. Rev. Lett. MERA: periodic chain of 4 spins. G. Vidal, PRL 2007.

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MERA in 2D ( Multi-scale Entanglement Renormalization Ansatz )

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  1. MERA in 2D( Multi-scale Entanglement Renormalization Ansatz ) Łukasz Cincio (POSTER) Jacek Dziarmaga Marek M. Rams (POSTER) @ Uniwersytet Jagielloński arXiv:0710.3829 accepted in Phys. Rev. Lett.

  2. MERA: periodic chain of 4 spins G. Vidal, PRL 2007

  3. MERA: from N=4 to N=8 spins

  4. MERA representation of a quantum state on 8 spins

  5. MERA: entanglement renormalization (real space renormalization group on a quantum state) G. Vidal, PRL 2007 on 4 block spins on 8 spins 1st decimation

  6. MERA: entanglement renormalization on 2 block spins on 4 block spins 2nd decimation

  7. MERA: entanglement renormalization on 2 block spins 3rd decimation

  8. MERA representation of a quantum state

  9. MERA: entanglement renormalization in critical quantum Ising chain G. Vidal, PRL 2007

  10. MERA in 2D

  11. MERA in 2D: quantum Ising model

  12. MERA in 2D: results

  13. Conclusion • Symmetric MERA in 2D • & • First test in 2D with encouraging results Work in progress • 2D t-J model Łukasz Cincio (POSTER ON MERA ) Marek M. Rams (POSTER ON ENTANGLEMENT IN KIBBLE-ZUREK MECHANISM)

  14. MERA: expectation values

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