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Renormalization of Entanglement in quantum spin models

Renormalization of Entanglement in quantum spin models. Sharif University of Technology Department of Physics. R. Jafari , M. Kargarian , A. Langari. Outlines:. Motivations Quantum Renormalization Group RG of Entanglement conclusions. Motivations.

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Renormalization of Entanglement in quantum spin models

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  1. Renormalization of Entanglement in quantum spin models Sharif University of Technology Department of Physics R. Jafari , M. Kargarian , A. Langari

  2. Outlines: • Motivations • Quantum Renormalization Group • RG of Entanglement • conclusions

  3. Motivations • entanglement is the essential resource for quantum information processing and quantum communication. Protocols based on entangled states can offer an exponential speedup with respect to classical computation. • entanglement measures quantum correlations for pure states, it is natural to think of a close connection between entanglement and the correlation functions of highly correlated states in condensed matter systems.

  4. QRG • In condensed matter physics, we are faced with huge number of particles. • Diagonalizing the Hamailtonian of the quantum many body system: • Dimensionality of the Hilbert space:

  5. QRG • Resorting to the approximate methods are unavoidable. • QMC • QRG Hilbert Space Effective Hilbert Space Physically Relevant

  6. Mathematical Framework • A prescription is that Block Real Space RG

  7. Real Space RG • So an implementation of RG: • Reduction the size of the lattice • How many sates to be retained in the truncation procedure

  8. Real Space RG • Block RG or coarse graining J J J J J J’ J’ J’=R(J)

  9. ITF Model H= HB= HBB=

  10. ITF Model

  11. ITF Model

  12. XXZ Model

  13. Entanglement and QPT ITF Model A. Osterloh, et al. Nature, 416 (2002) 608

  14. Renormalization of Entanglement in ITF

  15. Renormalization of Entanglement in ITF

  16. Renormalization of Entanglement in ITF

  17. XXZ Model

  18. XXZ Model

  19. summary • Tackling the quantum many body systems in condensed matter physics from the quantum information perspective deepen our understanding of exotic states of matter. • We combine the quantum renormalization group notion with the entanglement in order to study the entanglement in some quantum spin models. • Evolution of entanglement through the renormalization procedure truly captures the critical behavior of the lattice models.

  20. Thanks for your attention

  21. Mathematical Framework

  22. ITF Model

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