Renormalization of entanglement in quantum spin models
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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

Renormalization of Entanglement in quantum spin models

Sharif University of Technology

Department of Physics

R. Jafari , M. Kargarian , A. Langari


Outlines
Outlines:

  • Motivations

  • Quantum Renormalization Group

  • RG of Entanglement

  • conclusions


Motivations
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.


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:


QRG

  • Resorting to the approximate methods are unavoidable.

    • QMC

    • QRG

Hilbert Space

Effective Hilbert Space

Physically Relevant


Mathematical framework
Mathematical Framework

  • A prescription is that Block Real Space RG


Real space rg
Real Space RG

  • So an implementation of RG:

    • Reduction the size of the lattice

    • How many sates to be retained in the truncation procedure


Real space rg1
Real Space RG

  • Block RG or coarse graining

J

J

J

J

J

J’

J’

J’=R(J)


Itf model
ITF Model

H=

HB=

HBB=





Entanglement and qpt
Entanglement and QPT

ITF Model

A. Osterloh, et al. Nature, 416 (2002) 608







Summary
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.





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