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MERA in 2D ( Multi-scale Entanglement Renormalization Ansatz ) Łukasz Cincio ( POSTER ) Jacek Dziarmaga Marek M. Rams ( POSTER Uniwersytet Jagielloński.

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Presentation on theme: "MERA in 2D ( Multi-scale Entanglement Renormalization Ansatz ) Łukasz Cincio ( POSTER ) Jacek Dziarmaga Marek M. Rams ( POSTER Uniwersytet Jagielloński."— Presentation transcript:

1 MERA in 2D ( Multi-scale Entanglement Renormalization Ansatz ) Łukasz Cincio ( POSTER ) Jacek Dziarmaga Marek M. Rams ( POSTER Uniwersytet Jagielloński arXiv: 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) 1st decimation G. Vidal, PRL 2007 on 4 block spins on 8 spins

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

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

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 Work in progress Symmetric MERA in 2D & First test in 2D with encouraging results 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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